Stock wheels are 13x5.5.

A lotta people run 13x7, and that's the max size allowed in some racing classes.

If I were to mount the same 205-60R13 tires on either wheel, what kind of differences in behavior would I notice?

Would that 1.5 inch difference make the sidewalls curve in an unsafe manner or perhaps make it more prone to unseating the bead on hard turns?

Would the difference in sidewall angle make the handling feel better?

 

I cant remember where, but I remember it being stated that a 205/60 tire is perfect for a 7" wide rim. I wish I remembered where I read it, because it was even specific to a 13" diameter rim (if that matters).

I am sure it should be fine though, 205mm comes out to 8", so the tread width is gonna be wider than the wheel either way. Id have to say it almost seems a 205 is more suited to a 7" wheel than a 5.5".

 

The Legend car series uses a 205/60-13 on a 13 x 7 wheel. That is the only setup allowed to be used. I suppose they have reasons for mandating this setup.
5.5 width wheels will actually make the tread tend to bulge in the center, thereby reducing the available footprint.

 

The 205/60/13 tires will tend to flex too much, the only thing you can do to help compensate is to over inflate the tires when using the stock 5.5 inch rims. The best tire suited for the stock rim is the stock size 185/70/13. The wider wheel will feel much better with the 205/60/13 tire.

For autocrossing the 13x8 wheels with 225/45/13 tires seem to be the choice.

 

I have a set of mint Revolution wheels, these have become pretty rare.. As near as I can tell, they are 13X8.5, may be only be 8" wide. Spokes are painted silver, the rest of the wheel is polished. They have Hoosier autocross tires, 225/45/13. If these interest you, or anyone else, I'm looking for 600+ shipping. They come with studs and lug shank nuts, sorry, no center caps. The Hoosiers are old and one has the cord showing, tires are optional as I don't know how well they will hold up or provide traction due to age.