I've only driven a UK 200SX S13, and an S14a but the same should appy.
Feels a bit more of a grand tourer. It will feel a little bit "tall" and less responsive than the Integra, and NOTHING like the AE86. Chalk and cheese! Far more insulated. Turn in is still pretty good but they can wash out a bit mid corner, sometimes don't feel totally planted, similar to driving on wet grass or ice only far less pronounced of course. I'm told coilovers or very good suspension kit normally sorts this out.
Engine is a little bit flat as standard but responds really well to breathing mods and tuning in general. Talking about the SR20 here not that nasty thing that belongs in a chainsaw (CA18DET)
Easy peasy to get them sliding, especially with an LSD.
Pretty robust motors even when tuned but not unburstable, look out for turbo gaskets going (not expensive just a long job to do), bottom end rattle is definitely a weak spot, seen a few head gaskets go too but if anything it'll be those big ends.
Capable of stupendous rot - sills, panels, wings, front panel, inner sills etc.
I really do like the S13 Silvia shape (both the nose and that funky notchback) though I do prefer the Sileighty just a little bit.
Just as overpriced as the AE86 IMO, remember what you are buying is essentially a 200SX with fixed headlamps and a 2.0 engine. S14 and 14a represent much MUCH better value for money but like you theres something about the look of the S13 that I just think is "right"