I used to use Dawn. It worked OK for polishes, but it takes forever to get the pad 100% Dawn free. Some pads (Hydrotechs), its almost impossible to get all the Dawn out. I made careful inspection of this by wringing out a Dawn cleaned pad in a glass. Then I compared the wrung out liquid glass to a glass filled with water from the same source. The glass from the pad always makes bubbles. So, I stopped using Dawn
Then I started using Blackfire Pad Cleaner. This stuff works very well for polishes, and very well for some LSPs. The only issue with it is it costs a lot. I've also tried the DP/WG powdered pad cleaner stuff. I use this stuff as a pre-soak. Honestly, it doesn't perform too well for me. Even mixing it as an ounce to 32 oz its bit that great.
Then, I started using LA Awesome to clean pads. Its pretty cheap, you can use it liberally. This works as well, if not better than the BF pad cleaner. In fact, it sort of feels the same on your hands. I wouldn't doubt if they both contain similar ingredients. The LATA, is a little more work than the BF pad cleaner to get out of pads 100%, but only a little. Its less than 1/12 the price of the BF stuff. I buy many bottles of LATA at a time and dump them into a gallon container.
I've also have a few bottles of the WG Pad Cleaner & Extender. This works well, but not as well as the BF stuff. Again, I use these products liberally, so they get pricey.
So, I'm sticking with LATA.
For waxes and LSP, nothing works as well as mineral spirits and IPA. If you think your wax pad is 100% clean, squeeze it in some mineral spirits and you will see the carnauba quickly come out and cloud up the solution. MS followed by IPA will get the most difficult LSPs out of your pads 100%. Of course, its time consuming and can get expensive, some may just choose to throw the pad out or leave wax in it.