Here is my own idea, how I’d tier the characters by their level. The tiers are chosen by comparing the levels of pure-classed characters and how their options and enemies measures them. I think that some certain levels will make a bigger difference in most class than most. There are only small differences between the official version and mine, but nonetheless enjoy.
Amateur Tier (1st-2nd level): These levels are more for expressing some people, which decides to go adventuring without any real experience. The characters have so few features and options, dries out very fast, are being killed when full by an unlucky roll, that you can only think: These guys have either never faced real danger or lost their powers due magic, injury, etc.
Beginner Tier (3rd-4th level): The character won’t be one-hit-killed, there are some more resources and every character will have a subclass (at least the single-classed ones). You may believe, that these characters survived an adventure, but they’re still wet behind their ears. But at least they’re now on a professional level and can live their lives as full-fletched adventurers. Well, there is a saying in the forums, that 3rd level is the new 1st level. 😉
Heroic Tier (5th-9th level): This was hard, but I set it on 5th level for two reasons: Extra Attack and 3rd level spells. Since the first one is an important factor which separates weapon-focused classes to those who are not and the latter brings a lot of new, but classic spells into the repertoire, these should be the level-range of most adventurers should be. Some are more experienced, some are not, but even 10th level characters are more to be considered as ‘strong’ instead exceptional. And with 5th level spells, you have the most basic ones, since you might regain them by class features.
Legendary Tier (10th-16th level): Here you are the stuff of legends. Most classes will grant you some real cool benefits at 10th level, empowering your character to different degrees, depending on class, but at least be useful. For other classes 11th level would be the real border-level, but I decided after quantity. Only few will have these levels and most of them are people, which deeds are well-known in their region.
Master Tier (17th-20th level): Here you gain a great mastery of your class, getting access to 9th level spells, while most classes get powerful features at 17th level as well, here nobody will doubt, that you’re an outstanding individual, whose decisions will make massive waves (like letting the local king think that you’re threatening his kingdom with some sort of plan, while you just decided to spend your vacation there).
Epic Tier (21st+ level?): Since there were rules for characters above 20th level in about every edition, I’m sure the DMG will provide us again with the wisdom and rules to play someone stupidly powerful. More like a powerfool.
With this I think I (and I hope you, too) will have a better grasp about how experienced and powerful the characters (and monsters, even though you shouldn’t use their CR, but more hit dice or caster level) really are.