Well, it's been done loads of times here on Y!A, so it's possible in itself.
But if you're talking of the merits of comparison, it would still depend on who'd answer your question. I haven't read Twilight but I can still compare even on just the subjective basis that my whole family shared Harry Potter even my husband who doesn't read fiction. But I doubt if he'd read a teenybopper one like Twilight. I could imagine his eyes rolling all the way to the ceiling.
You're right about the universe thing there. JKR gave us a new and ingenious presentation of the magical world we all know ourselves since childhood but she did it in such a way that people got immersed on it. We all grew up with Cinderella and Snow White and the wicked witches and mermaids and the whole hoolaballoo of fairytales but people didn't have that hunger to learn how come the witches came to be that wicked, or have lingering questions on what happens after that "happily ever after" note.
HP fans are in a new genre of their own. HP's world is no Middle Earth and undoubtedly, Tolkien is a far better writer than Ms Rowling but she also created a phenomenon, there's no doubt about that. Even with the "hotness" of Edward and Jacob and everyone else in Twilight, it would still be just a teen romance story. Though the number of fanbase cannot be denied, it would still be millions behind HP's.
HP has cut across age, gender, political, economic, cultural and even religious boundaries. Unless, you can get my husband to even read it, I couldn't say the same about Twilight. And my 7-year old son (with Global Development Delay) would insist Edward to sport a cape, otherwise he wouldn't believe he's a vampire. LMAO!
So there, it IS possible to compare Twilight with Harry Potter. LOL!