Autocrossing can work with a bit overly wide tire better than road courses likely due to not staying in one direction for very long and the pace is so quick you have less time for the sidewalls to move, load up the suspension, etc like on long higher speed corners on a race track.
I just looked up the specs, the 225/50/16 is very tall at 24.7" but sometimes taller is better to keep you in second gear and off the rev limiter. If you are in a class where you can tune the car then it can be raised significantly and safely so you can run the shorter tire and save weight, rotational mass to stop and start moving, etc....
225/50/16, 24.7" tall, 8.8" tread width which is a very wide 225 and would be best on a 9" wide wheel for road racing and perhaps autocross.
9.4" section width, this is a very wide 225 and going to be a bit "pinched" on an 8" wheel, 9's if allowed require a rear camber change.
21 lbs with much of the weight far out from the center of rotation.
205/45/16, 23.0" tall, much easier clearance, a bit shorter than stock, would require more shifting unless you can raise the rev limiter in your class.
8" tread width is great on an 8" wheel, 8.5" section width, this is a very good fit on an 8" wheel, outside to outside the bead measures 9" on an 8" wheel. Just a tad bit of stretch which will provide much crisper turn in, feedback, quicker lateral transition.
17lbs, 4 lbs per corner less weight is a huge performance enhancement.
I know what tire I would pick, not the 225.
As an example of side wall specs not meaning much when picking tires, the 225/50/16 Bridgestone RE71R, one of the top max perf summer tires.
7.6 tread width, 9.2 section width, 24.9 diameter, 24lbs.
The only consistent spec is rim diameter, the rest can be about anything they want to put on the sidewall and dramatically different in reality.
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I have not won a title in Autocross since the 70s's, we had our own regional organization, SCCA was not in the area. Since then I have built several fast cars the way I wanted them then ran the class they fell into, taking 2nds and 3rds in the wrong car for the class has been more rewarding to me than building the best car and winning easily, which I did in the 70's. First FWD was the first 1zz turbo Matrix ever done, not as good a car as this one for sure, far fewer mods than my ST, less power, still was second fastest SM class car in SoCal which means it was very quick as ran against RWD and AWD. Just saying these things to show I have a bit of experience in FWD and autocross and decades of researching tires.
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All that said, the taller wider tire could still end up being a bit faster with the right driver, setup, etc...but likely it will be much more difficult to extract any benefit on a wheel not of optimal width for the real specs of the tire.
Hope this helps, that is the intention as always

Rick