Why is The Princess and the Frog constantly overshadowed by Tangled?

The problem with PatF is less that the story is too complicated, but that it doesn't make much sense (too many plot holes). I disagree with you about the climax..due to the messy plot of PatF, this movie has no less than four endings, and the "final battle" isn't really that exciting, even with a death thrown in. In Tangled, we get both main characters being ready to sacrify everything for the other, and with "You were my new dream" a truly romantic and memorable quote. I also disagree about the villains, but even if Mother Gothel were "bleh" and not one of the few Disney Villains with a really interesting motivation, she would be still better than Facilier, because he has not connection nor any real interest in Tiana, and Naveen just becomes his victim by chance. If there is no personal connection, defeating a villain is less satisfying for the audience.
And finally: People might complain about the songs in Tangled (though I don't agree there either), but the movie has a great score. The music in PatF is boooooring, and the songs mostly utterly pointless.
And no, PatF didn't renew anything in me...I was just glad that the Disney Animation Studios were back, but when I saw the result, I was disappointed. With Tangled, I felt the Disney magic again. It was stunning, it was inventive, it was a very good adaptation of the original fairy tale, it was revolutionary in terms of animation, it was basically everything I expect from a DP movie.

Simple, because Tangled is a better movie. This isn't matter of opinion, because Tangled is the better film in almost all aspects. The characters are more consistent and interesting with realistic arcs, unlike in PatF where there's like four different versions of every main character except for Lottie, and their arcs make no sense (how does Tiana fall in love with Naveen again?); the plot makes sense, unlike PatF which is a convoluted mess; the animation is revolutionary, while PatF is typical annimation; the songs might be worse than regular Disney house, but they do grow on you, where as the majority of PatF soundtrack is horrible (this is coming from someone who adores Jazz); the villain had real motives, while we never do figure out what Facilier wants; the love story is well paced and equal on both sides, where as you can see when Naveen fell in love with Tiana, but we don't know why, and we never see Tiana really fall in love with Naveen. Overall, PatF is a mess. And trust me when I say I'm not biased, because I like PatF considerably more than Tangled, but it's quite easy to tell more care and dedication went into Tangled, whereas PatF was Disney's solution to the racism claims.

I must agree that I don't see what makes Tangled so incredibly better than PATF, but I will admit that Tangled is objectively the better movie, but only by a little bit. I pretty much agree with what NostalgiaCritic has to say on the matter- Tangled has an amazing plot with mediocre/ good everything else (ok, objectively the animation is AMAZING, but most people prefer 2D, at least in my experience) and PATF has great everything else (well, maybe not music, but I like it, and it least makes sense why that is the style, unlike in Tangled) and a mediocre/ bad plot. Together, I think they could have made an awesome movie.

The problem with PatF to me is the infinite number of incredible and refreshing ideas and concepts that never actually got the proper and accurate effortful realisation and development. Rather than focusing on Tiana's passion and investement in her dream of owning a resturant and achieving this goal on her own seeing as she was initially presented in the movie as a "strong independent" type of heroine the movie chooses to thrown in the sequence with a random talking frog offering her a bunch of money - without providing any sort of proof that he actually does have said money - and our "strong and independent" carelessly agreeing to kiss him which not only comes off as inconsistent and an unbearably contrived plot device in order to set the events of the story in motion, but generally offensive in relation to Tiana's character due to sending a message of a working class woman being essentially incapable of accomplishing anything unless an obnoxiously arrogant son of royalty ends up by her side... which is not what happens after she kisses him, but what the entire plot eventually comes down to by the end. Naveen, contrary to Flynn, gets virtually no evident character development nor comes to respect women in general. Starting out as a spoiled narcissistic kid who wants to marry for money he intends on using a wealthy girl's naivety and life long dream of marrying a prince in order to keep living a lavish and careless lifestyle instead of getting a job and supporting himself. By the end, Naveen is ready and willing to consciously propose to a girl with the same intention of using her as a money bag which was the initial plan only this time he had an additional goal of founding Tiana's resturant and keeping his promise to her, by that point already being in love with Tiana which only makes his proposal to her best friend who he doesn't love or even know/care about in a slightest a thousand times worse, all of it occurring after the supposed mentality and attitude change that happens literally over second with no basis or substance to it other than Tiana explicitly and openly telling him about how lazy and useless he is after he deliberately and directly mocked her working class by disdainly referring to her as "waitress" due to his general tendency to humiliate people of a lower social standing by either picking on their lack of privileges or other things that Naveen found particulary annoying (such as Tiana not fitting into traditional standards of having fun therefore being "boring") or even body shaming which he continuously confronted his servant with (and judging by Lourence's further statement, the humiliation on Naveen's part was a common practice and the essential attribute of their relationship, which was eventually brushed under the rug by the movie due to Lourence being conveniently villianized).

It's because Rupunzel was set free but princess in the frog Tiana has set her goal and meeting it so tangled doesn't really over shadow princess and the frog

I'm guessing people Liked Tangled more because it reminded them of the classic films they used to like in their youths- Princess Bride, the old Disney films...It has a lot of charming elements that fuel anybody's passion for these type of stories.

I also think, for the typical audience that watch these movies, the characters are much more...relatable? And that's the big thing with characters nowadays. Most people can relate with Rapunzel's cuteness than Tiana's hardworking attitude, and most people daydream about having an adventure in a "magical" fairy talle-ish land over trekking in the swamps of Louisiana.

As for why PATF isn't popular...Dunno. People are quick to pull out the race card (and i can agree that i see some people not wanting to like this movie because of Tiana being black), but it also happens that PATF is in the middle of the road. It's cute, but nothing really that groundbreaking when compared to, say, Little Mermaid or Beauty and the Beast (talking about movie only-terms. in social/progressive terms is very different). A black princess is very good to have, and we needed one, but I think she came a little too late? In the time to be that relevant. Maybe if PATF had starred in the 90s she would've made a bigger impact...

Outside of that the story is very kinda "meh", and while i love the characters and the animation, Ii can see why people prefer Tangled (everybody prefers CGI nowadays) And it just so happened that it came out at a time where Disney wasn't doing too good (their last hit was Lilo and Stitch, which came out in 2002, and PATF in 2009...7 years of "meh"-ish underwhelming movies for the general public, it isn't hard to think Disney was losing its charm), and it competed against Avatar at the same time...

I think that would work for the movie's advantages is cut down all those swamp scenes tbh. They just dragged the movie down.

As for why Tangled is popular...I think people just prefer CGI animation over 2D nowadays. People like characters like Flynn and Rapunzel, and they just like the "vague european fairy tale land" aesthetic of Tangled over the clearly USA/New Orleans look of PATF (I guess, I remember speaking with spanish Disney fans about PATF and they didn't like the idea of a fairy tale based on the USA for some reason, they found the concept too "Modern" and not magical enough, despite the core of Disney being 100% americana (Walt was such an american boy, you can even taste the americana feel in stuff like Mickey and Friends)).

And while both films don't have the best songs, Tangled kinda wins with a better story. Less plot holes and more consistency. PATF has an interesting story but the ending is like divided in four parts and the swamp scenes drag way too much. The villain also doesn't appear much in the film, which may also sour some people (often the villain is the most memorable part of a Disney film).

I think this happens every time a new movie comes out. Tangled was overshadowed by Frozen, and Wreck it Ralph by Big Hero 6. Not to say these aren't still good movies, but it's still pretty easy for them to get overshadowed. Each movie that comes out somehow overshadows the last, it rather is "This movie is so much better than that movie!" or it becomes so popular that people start to say "What the heck? That movie is so much better!" Unfortunately for the Princess and the Frog it was the first one. It seems like people are so worried about the new movies or so excited that the ones that were just the new ones get forgotten. But I agree, it's annoying. Trust me I always like unpopular things, but don't let it get you down:)