See the title - are there any show-stopping differences between GNOME and KDE, at this point? Is it just a matter of preference? I know some applications run 'better' one or the other, but besides that, are they each geared towards something specific?
No significant difference. And I should note – Gnome and KDE are desktop environments, not window managers. Window managers sidestep the issue of UI integration, etc. in the first place, because they aren't bundled with other software.
As you said, if you care for UI integration, I always look at the applications when deciding which one to use. (I switch quite frequently.) In all honesty, I currently use KDE because I feels that its file browser and text editor, Dolphin and KWrite, are more powerful than their Gnome counterparts, Nautilus and gedit.
None of that really matters though, since both desktop environments now have support for emulating the other. Though in fact, I'm typing this in an unthemed, GTK-based Firefox. So, my answer is no, Gnome and KDE are not worlds apart in terms of functionality.
Two years ago, I would have said Gnome prefers simplicity while KDE prefers customizability. But KDE 4 changed things greatly. KDE is now a little flashier than Gnome, but beyond that, they're essentially the same.
To add to what Nikhil said:
Well, I think one of the main things that differentiates KDE and GNOME in particular is that GNOME is aimed at making things easy and straightforward, at least from their point of view (I say this because there have been many arguments amongst the developers from both camps as to what is 'easy and straightforward'). KDE on the other hand seems to give users a lot more options. What's interesting is that if you're in any way comfortable with computers, it might end up being that KDE, with its more options, would seem easier for you since you have more possibilities in terms of customizing things to your liking, whereas on GNOME you might be wondering where or how you do a certain thing.
But yeah, I think the only difference is the ideology and goals of both projects, and whether or not they match your way of working or perception of using a computer. Nowadays, programs written with a particular Desktop Environment over another still seem to work fine on the other, so it really does seem to come down to personal preference.
I personally have gone back and forth between the two, but I believe I've used KDE when I work as it feels a lot more versatile, in my particular experience of course. For simple browsing and computer usage, GNOME feels comfortable and easy.