I had a 2005 Tiburon SE for almost 6 years prior to the Z.
1. FWD is so much easier and more forgiving in bad weather. Not to say the Z can't deal with bad weather but FWD deals with it better.
2. Also the 2+2 layout means you can technically take 4 people if you had to.
3. A trunk to put stuff out of sight.
4. Regular maintenance and gas was much cheaper in the Tiburon. Cheap gas, cheap oil, cheap tires etc. Insurance wasn't much different.
A few things that are the same. Modding and aftermarket parts are expensive when compared to more common sports cars. Tiburon had clutch issues wearing out early (IMO was from driver inexperience) so does the Z the CSC (concentric slave cylinder) on the clutch fails on many cars.
One thing I did like coming from the Tiburon was it used a timing belt which was a pain to change, the Z uses a chain which doesn't need service.