Well, I'm originally from NYC, but I just came back from Chicago. I have to agree that a GOOD New York slice is hard to beat.
It has to do with that experience of walking down the street and smelling that pizza fragrance wafting over the sidewalk, so you go in and get a hot slice and gobble that floppy thing as it completely burns the roof of your mouth. But...it...hurts...so...good...
Now, I've had a few different kinds of deep dish -- from Pizzeria Uno (original, I believe), to Lou Malnati's (Uno deserter?), to Giordano's (another Chicago chain), etc. Actually, they all have their own distinctive characteristics, but they share the same basic idea: they use a "shorter" crust (more butter -- flakier) to hold a deeper portion of sauce, cheese, and ingredients.
It's constructed more like a traditional pie versus NY pizza, which is more like a tart (or stuff spread on a flatbread, basically). Anyway, it's really a fork and knife meal, and it's a totally different deal, so I think you really can't compare the two.
Like I said, I prefer a good NY slice, but a good deep dish can be satisfying when you're in the mood for that, too. It's just not conducive to eating on the fly.