I like both, but only when they are done well.
When I just started playing the Sims 4 I use only alpha, but now I started to like maxis match more and downloaded tons of MM ccs. I still use both in my gameplay and I don't think the alpha ccs I have look out of place. To me, maxis match hairstyles are adorable, they come in styles that I would like for my sims to have, and they cause less lagging, but alpha hairstyles have more variety in length and style that I can use them to achieve looks that MM can't achieve. I know there are clayfied hairs but I don't really like them. They look rather 2D than 3D to me (although there are some nice ones too).
For skins, I think some alpha skins that does not work with the game skintones and make sims look extremely white or pale are creepy. Most of my skins are maxis match. Even if I use an alpha skin I would choose an overlay that works well with the game skin colors. I do prefer more realistic makeup, but not way too realistic. A lot of alpha lipsticks look too shiny and pasted so they are out of question.
For clothing, I prefer MM, but there are some great CC creators who create very high quality alpha clothing that does not look pasted or paper-like and fit into the game as well, so I use their works too.
I agree with what Cyrus said above that alpha cc has a bad reputation because there are so many questionable pieces of cc. In my experience, alpha cc do cause a lot more problems, and some alpha cc really don't look as good as they are in preview pictures. With alpha cc you probably need to organize your CC folder more often and delete those CC that look terrible or out of place.
Again I feel like it is unnecessary to fight over this subject, or judge people base on what CC they use. It's nice to hear everyone's opinions though.