Which one is more reliable? There are 1000s that I cannot solve, and 1500s and even 2000s I can easily solve. I used to think that ratings was the measure of skill, but recently it seems that looking at the number of correct submissions for problems is proving a better measure for me. Am I mistaken that a 1000 rated person should be able to solve all 1000s? I am now ranking myself based on submission number now, and it has proven far more useful in searching for problems my level. What do you guys think?

A user with rating X should have a 50% chance of solving a problem with rating X in a contest (see this blog for more information). In general, older problems with the same rating are easier/more standard than newer problems with the same rating, but newer problems might have more solves on average because there are more contest participants now. No method is 100% reliable when it comes to knowing how hard a problem will be for you, so don't stress too much about knowing the exact difficulty.