I don't remember to be exact. There was a few episodes involving them both when they're young, but I don't know who's older.

burns looks older

i guess..

Actually it's kind of an unknown, they both served in World War II together and in the same unit, The Flying Hellfish, and in that episode, Abe recalled that Burns was of a lower rank than him so it could mean Abe is older than Burns, but then again, Mr Burns had his 7th college reunion in 1938 which means he graduated in 1931-1932, so I guess no one really knows exactly but they seem to be only a few years apart.

The age of Mr. Burns: 124 years!!

I cant remember which episode but I recall one episode with grampa saying his age and he isnt really that old (well to me he isnt but really he is not as old as mr burns)

totally mr. burns cause isn't he past 100?

104?
That was said in an episode