Bill, the cons of chlorine tabs far outweigh anything compared to regular bleach. Bleach is just about the purest form of sanitizer you can put in your water. I know we think of it as strong because of the daily uses around the house, but it's still mostly sodium hypochlorite - same as liquid pool chlorine (same thing). When used is the proper amounts as seen on the Chlorine/CYA Chart (link below) it is totally fine for the swimmers and pool equipment.
Tablets on the other had are made not only with a sanitizer, but also with stabilizer which drives-up your CYA. Before you know it, you're hearing those awful words "drain your pool" - the only way to reduce excessive CYA. Tablets are fine for short-term use, areas with a short swimming season, or folks with a high water turnover rate, but for the most part, we recommend regular bleach for those who manually add chlorine. Of course some people will invest in a salt water generator (SWG) that coverts salt to chlorine.
But when used properly according to that chart I spoke of (linked below), it's absolutely fine. I hope that helps answer your question.