I have been using Ballistol for a couple of years, and come to a similar conclusion about its strengths and weaknesses. It's definitely good for dissolving carbon. It doesn't damage polymer, wood, or other materials of your grip, stock, etc. It isn't going to poison you if used indoors while not wearing gloves. I'm skeptical that it does anything to remove lead from barrels, despite what hickok45 says. I am pretty sure it does absolutely nothing to remove copper fouling. I've seen some heat tests on it, and read its MSDS, and it appears to have a relatively low boiling point, and turn to black goo at a fairly trivial temperature.
Break Free CLP works okay. I have one small bottle that I used on my slides. I decided a while ago I wouldn't be using anything with PTFE in any high temperature locatiions, especially inside the bores of my firearms, since it can convert into corrosive and poisonous substances under high heat. There seems to be a lot of confusion about which version of Break Free CLP has PTFE or not. The bottle I have says it has PTFE on the label. So I have used it a fair amount on the slides of my pistols and it works pretty good for that, but I don't use it on the barrel, so I can't speak to its performance there.
Eezox I just started using a couple of months ago. Eezox has a solvent that is highly toxic, so I wear gloves and apply it outdoors. Once the solvent evaporates, I think it is fairly safe. It seems to work okay for carbon cleaning, but I don't know if it does anything to lead or copper in the bore. Its main benefit is forming a dry protective layer after you're done with it.