Should I watch FMB after watching Full metal alchemist?

It's fun.. Watch it...

Actually, go read the manga! FMA has the best manga ever!

Weeeeeell now, I'm glad you asked. Achem. I'll try not to take up too much of your time with a 5 paragraph response.
For one thing, pokemonfan909 is absolutely correct. Read the manga, it's amazing. Brotherhood, is basically the animated version of the manga. About halfway through the first series (roughly whenever Wrath was introduced) FMA completely went off from the manga and created its own story, resulting in... well... that ending. Once the manga was finished, the author asked for a recreation that was more loyal to her work, resulting in Brotherhood. It's the same anime for I'd say 2 seasons/a season and a half. After that, the two are completely different, including some of the Homunculi's identities. It's a much better series in my opinion with a truly satisfying ending. Either the manga or Brotherhood are worth it, but if you liked the first series, I really recommend the second.