Going to have to see the PHB before I decide on either. But probably I will allow both.
I've always liked 3e style multiclassing when it made sense in the narrative of the game. If your fighter decides to take up wizardry full time, it made sense to me. Dipping into a level of this or that to qualify for a prestige class or to optimize bugs me, but as long as you justified it with some story, I was still ok with it, even if it was a thin excuse. Optimization is just how some players love to play, and as long as they give a nod to the story, it's all good.
Now with the more flexible subclasses such as eldritch knight, I think that more players will go that way instead, so we will see less multiclassing. Probably I will decide on multiclassing on a case by case basis rather than a blanket ban or always allowing it, but if I like the rules enough then maybe I will just allow it, since my players tend not to ignore the narrative.
Of course I will always reserve the right to say no; sometimes it just doesn't make sense. In particular I don't like the idea of someone taking more than two classes. It's not a skill based RPG, and that just doesn't work well IMO.
Feats look good from what I've seen; I will probably allow them. I see them as good options for customization. I don't think I will allow any feats outside of the PHB except on a case by case basis though; I very much disliked the huge list of feats in 4e.
Glad to see multiclassing and feats are officially optional. Yes the DM can change anything, but when a system is designed to be optional it makes it easier to ban things you don't like, or add things you enjoy. Modularity is one of the big appeals to me in this edition, and I hope many systems are easily ignored without having to redesign the game.
I think one of the problems with D&D is not with the balance and functionality of combining all the options in the core rules, but with the plethora of classes, feats, spells, etc from other books. To protect my wallet and sanity I plan on limiting my source book purchases and keeping the game mostly core. While this is not the first time I've made that plan, this edition has so much variety in the PHB I might actually stick to the plan this time.