У тебя is more natural in Russian, and generally something you can hardly ever go wrong with. There's no difference if it's a statement or a question.
If it doesn't sound like the most obvious way to say it, consider the fact that in English, too, there's more to the "your" in "your dogs" than meets the eye. Namely: apart from indicating possession/relation, it's also a kind of stand-in for "the". What I mean by that is, in English, you always expect some word to go in front of "dogs" when they're "definite" dogs. Whether it's "the dogs", "your dogs", or "Jane's dogs". And so the "your" part is in that slot in the sentence which you expect to just be ticked off in passing, without putting a lot of emphasis on it.
Not so in Russian, where you can just say Собаки едят яблоки? to mean both "do dogs eat apples?" and "do the dogs eat apples?" Therefore adding твои in front of собаки actually feels like you're adding something, and therefore giving it some significance, pushing the whole thing slightly towards: "those dogs of yours, do they eat apples?"
Now the thing about у тебя is, it sort of applies to the whole of the sentence. Think something like, "do the dogs eat apples on you?" — which doesn't sound quite right in English, but the same general figure of speech is quite natural and neutral in Russian. Therefore, у тебя doesn't really emphasise whose dogs they are in a way that would require some justification in context, as with твои (say, "those dogs you're breeding/genetically engineering, do they eat apples?").
У тебя is a lightweight, in-passing addition because you never really don't expect it. It works with pretty much any statement. You can say У меня Рим победил Карфаген, literally ~"Rome has defeated Carthage on me", and there's at least one context in which it would make perfect sense: "I'm at the point in the history book I'm reading where Rome has defeated Carthage". You can think of у меня, у тебя, etc. as a way of "possessing" entire events, rather than their individual subjects or objects.
Hope that made sense. Arioch's answer probably deserves the checkmark, I'm just here with some follow-up ramblings.