To clean my tires I use two products:
- Optimum Power Clean
- Tuf Shine Tire Cleaner
I used Optimum Power Clean since before the Tuf Shine was introduced. For getting a tire perfectly clean, there is no equal - Tuf Shine is the best.
If you want something that cleans the tire better than just about anything on the market, save for Tuf Shine, then I think OPC is the way to go. There were threads of people cleaning tires with other APC or tire cleaners until white foam, only to hit it with OPC and see more brown coming out. Of course, currently you can clean a tire with OPC, only to hit it with Tuf Shine Tire Cleaner and see that it's not perfectly dirty.
Since your not looking to apply a coating, such as Tuf Shine's, then I don't think getting the rubber 100% clean is a necessity. The nice thing about OPC is it can be used for different tasks - including wheels (assuming they're clear coated, chrome, etc. not uncoated aluminum), interiors, paint, and so on and so on...
Personally, I use Tuf Shine every once in a while and usually hit my tires with OPC every other wash or so. My tires are protected with CarPro PERL (which I love) and they don't need reapplying for over a month - even when cleaning with a 1:3 OPC solution and a stiff-brissle brush.
Hope this helps and happy detailing!