I own both. The 710 is one of my very favorites; I thought I'd looove the 805, but in truth, it really hadn't grown on me.
The 710's G-10 is fairly smooth. Not polished, it has some texture; but it's not as grippy as, say Spyderco's textured G-10. The 805 seems a bit rougher, but that could just be because I've used the 710 a whole lot more!
Both of mine have satin-finished blades. The 710 has a slightly shinier finish, but both are quite nice looking.
The 710 packs the same edge length in a much more compact grip than the 805. The latter has the pivot set far back from the front of the handle, which makes for a better-supported pivot I suppose, but the 710 seems just as stable. There's no blade play in either.
The 805's grip has that deep finger choil, which makes it a bit more secure, but I find the 710's handle to be more versatile, more comfortable in various grips. The 710 also carries easier; the 805's "big black banana" shape takes up a lot of pocket, and it ends in a point that can be rather, er, uncomfortable in snug jeans.