The theory goes...
19" wheel is bigger, would have more metal, and therefore would be heavier. Plus, the greatest mass has been pushed out 1" and therefore has a greater impact on rotational inertia. So, it would be heavier and harder to turn.

That is the theory at least.
Still haven't seen any numbers to support it having any effect in the real-world though.

The only other difference (given the same width) is the thinner sidewall supposedly makes the ride harder because there is less air volume (or so goes the theory). The flip side to that is it might actually help the handling, as the thinner sidewall would probably give quicker turn-in and more steering feedback.

The only time I really noticed a big change in the wheels was my very first Mustang some time ago. I went from 15s to ridiculously heavy 18" chrome wheels on a V6. Then, I admit, I could actually feel it hurt acceleration. This last time, I went from 17s to "heavy" 20s on my 05 GT and I felt virtually no acceleration penalty, though they did firm up the ride a little bit (felt good in the turns, a little harsher through pot holes). The changes were minor at most though. Given the 3" diameter change, I would have expected a lot more of a difference the way some people talk.

In the end, this is all just analysis paralysis if you ask me (especially for a street car). But, it is fun to think/talk about when you are saving up money to make a purchasing decision.

 

Yesterday I drove a 2010 GT with 19" wheels for the first time. It was awesome. The ride seemed smooth to me, but the handling in the corners and the steering were noticeably nicer than my 2005 GT with 17s. I wonder if my shocks have started to give out. I've read some posts where the shocks on the '05s start to go around now for some owners. The ride is definitely firmer now than new. And when I compare it to a new 2010, I notice a world of difference. I can't wait for the 2011s to get here.