In general, it is less likely for the SGC insert to damage a card than a PSA condom or PSA loose fit. To date, I have had two PSA cards damaged within the case and no SGC cards. I have also owned many more SGC cards than PSA. I also personally really like the Beckett sleeve. Unfortunately, they have also had problems with many cards sticking to the sleeve.
Overal, there is probably little to no real and tangible safety difference between the three. The chatter is more political rhetoric than anything IMHO.
Good points from all. I have also heard that occasionally cards in the BGS holders stick to the sleeves. This might be an issue if the cards are exposed to heat. I guess the big three are pretty safe overall and each have their pros and cons.