I don't have any center caps, so I cannot help with that part of your question.
The wheels look dull because the clear coat and colour cost beneath it have aged. It is possible that either one has also cracked, allowing road grime to accumulate under the clear or colour coats.
As for the polishing out of the wheels, you can go with one of the two folloing methidsL
1. Mask off the the areas that you want to preserve. Use something fairly tough, like mutiple layers of masking tape, or vinyl tape. Then, after removing the centers (unbolt from the back), abrasive blast the areas that you want to polish out. Anything that can be used on aluminum can be used. Then, using wed/dry sandpaper, sand down the blasted areas progressively until you hit 1000 (suggest 400 grit, 600 grit, then 1000 grit). After that, polish out to a mirro shine using a metal polish. I used Flitz metal polish with their Buff Ball on a drill.
2. You could always just sand the wheels out, without the abrasive blasting. Will take a lot longer, but you won't have to mask off the parts you want to preserve. The remaining process is as above.
Method 1 is faster, saving 4-6 hours per wheel. You need to be careful with the abrasive selected. I used 70/40 crushed glass on the recommendation of Eastwood's technical support department. They said that soda blasting would work, but due to the toughness of the wheel paint used, the time would be very long. The crushed glass actaully does a good job on the wheel paint, while not chewing up the aluminum much. If you try this method, please remember to use proper personal protective equipment (blast hood, breathing mask, glovers, and long sleeve coveralls)
Also, note the some folks on the board do not agree with my method. My results were pretty good, though, and I am sticking with it. I do have some posts up with the resuts of both methods (the 5 on 5 using the abrasive blast method, and a snowflake using the sanding only method(.
P.S. I will be repainting the 5 on 5 wheels in the "webs" between the spokes black. I haven't yet decided if they will be flat black, or semi gloss black. The black "webs" will make the polished areas really, really "pop", You may want to consider this for your 10 spoke wheels.
P.P.S. If the picture of the wheel is on your car, you appear to have the forged wheels (tire valve is on the flat surface), which polish out exceptionally well to a mirror like shine.