LLoyds was a solid Bank who in good times wanted to merge with Halifax. As the Banking world started to go belly up the then Government decided to urge them to go ahead and take on Halifax. Not enough due diligence was done and it brought them down. However after getting rid of the Chairman they had enough resources to slowly rebuild and get out of the mire.
RBS unfortunately had Fred Goodwin - bit of a megalomaniac who made some very bad purchases, Charter One in US and ABN Amro, so when the fall came they were not in a position to get themselves out of it.