RBMK has no containment and relies entirely on control rods to moderate it. #3 exploded because the rods were removed, the uranium deformed from meltdown, and the rods could only be partially reinserted. There was no stopping it.
BWRs have containment and can passively cool to some extent (not completely dependent on control rods).
RBMK are cheap to build and capable of producing a lot of power but they don't have much in the way of safety features. They are very much part of the Soviet Union design mentality. BWR are very costly to build and have relatively limited power production capabilities because the containment is so large and costly.
Daiichi is the only case of leakage and most of it was because of all the spent fuel held on site and emergency gas venting to prevent a steam explosion (which happened at Chernobyl). All of the uranium is still contained within the facility.
Fukashima Daiichi had a primary containment vessel ("containment structure" in the picture above) with concrete
25 feet thick. Unit 1, which is estimated to have >70% melted down, only managed to make it's way 10% into that. BWRs are all about safety. It took mother nature's worst to upset that facility
Chernobyl happened because of stupidity (the Russians haven't made that mistake again). Fukashima happened because of a 9.0 earthquake which is firmly at the back of every nuclear engineer's/architect's mind in designing new power plants.
Nuclear is still by far the safest electric power source known to man.
The reason why Vogtle is getting passive emergency coolers is because the cost of installing and maintaining them is far less than dealing with the associated costs with a meltdown. These are a $25 billion investment, a billion now to save dozens or hundreds of billions of latter, is a good investment.
Also, the main defining feature of Gen III is that it has a 60+ year service life instead of 40+ years.