The GTI weighs about 300 lbs more than the Si, and you can feel it, but both cars feel like they handle really well (based on test drives in both with no salesdrone present). I found the Civic's steering to be better weighted and all of its mechanical linkages feel much more direct, especially coming straight out of the Miata.
The Civic has an LSD and the GTI doesn't, and most reviews say you can feel the difference on the track. You don't notice it on a test drive. What really sold me on the Civic is that it feels like it's carved from one piece of billet. There's a tightness to everything that is very impressive. It actually felt a lot like a higher-strung version of the RX-8, despite the fact that the two cars share virtually nothing in common.
S.