I'm not familiar with the ASME compact tables, but I did a quick Google Sucks search and they appear to be similar. Or the Table of Contents does anyway. I like them better than the MERM, however, because there is more data points and it's easier to flip through. If you already have the ASME compact tables, it's probably a wash whether the book I have is better or not.
Problems...yeah, I've gathered they're much tougher than exam problems, but still teach good skills to obtain. There are times when I have to stop and ask myself "why." To make sure I understand why we're chasing down a lot of info. I think it's easy to get overwhelmed with the amount of work in each MERM problem, but important to step back and say, "ok, why did we just do all of that. If they gave me all those variables, would I know to use X equation to solve it."