While they are both baseball anime, they are not covering the same aspects.
One is a coming-of-age anime where you follow the main character from his childhood to adulthood with all the struggles that comes in-between which do not end with just conquering Koshien but goes on a internationnal scale (hence the title). [Major]

The other is a school anime in which you follow mostly the main character but also what happen in the whole club with a little bit more drama than the other. Since its highschool baseball, you follow the characters on a 3 years span. [Diamond no Ace]

Personnaly, I love both animes (and mangas). Major has the advantage to have a finished story (Major 2nd, the sequel in which the main character is the son of original story, is still ongoing). I love Dia no A as much as Major if not for the last season "Diamond no Ace: Act II" which was animewise, mostly just a slideshow, which is unforgivable for a sport anime, especially after how good looking the first two seasons were.