It depends on a lot of factors. (The main one is actually your water hardness. Around here, the water is soft straight out of the tap, so that helps me a lot.)

I get the best results with Cascade Platinum paks, so I buy those. I have had inferior results with other detergents. (Kroger has a clone of the Platinum packs. I think it's pretty good as well, but I don't remember.) So I don't buy those any more, I buy the one that I know will work.

It is not a surprise that the paks work well. There are several ingredients that "like" to be formulated as powders, and several ingredients that "like" to be formulated as liquids. The paks can contain both. This is not possible for pure powders or gels, so that lets paks have more different cleaners in them. (I don't know what's going on with gels. I've never personally had good luck with gels.)

Consumer Reports has the objective metrics you are looking for.