As a personal preference... I admire you decision to write that rather than say that we should say which one is "better".
So yeah as a personal preference... Disney by far. I was basically raised on my older sister's entertainment products as a child, meaning that I watched The Lion King, Beauty and the Beast and The Little Mermaid on permanent loop (among other films like Matilda and Toy Story). She'll never forgive me for (perhaps) accidentally breaking our video of The Aristocats.
But honestly I find that many of Disney's older (i.e. pre-2000) films hold up in terms of me liking them. I love Snow White ATSD, Sleeping Beauty, Lion King, Beauty and the Beast, Mulan (surprisingly) for a few examples, I even like the Lion King sequel (though The Enchanted Christmas can burn in Hell).
Do TV shows like Recess and Kim Possible count, too? 'cos I love them.
Dreamworks on the other hand has a few films I really love, but I find the ones I dislike to be obnoxious or frankly depressing and shallow (Shark Tale and Shrek 4 respectively). Shrek was probably the first film as a child that I watched without inspiration from relatives over and over. A lot of them I just haven't bothered to see, and I just don't look all that fondly on them as a studio.
Compared to modern Disney (let's say 2009-now), I liked The Princess and the Frog and Maleficent and I absolutely adore Tangled and Frozen. As for Dreamworks, I've just not indulged much. I did like Megamind though.