This came up twice recently. Once with the mutual agreement to use
milestones in our fifth edition campaign on Roll20 and second when discussing Shadow of the Demon Lord that some other friends are thinking of running as a summer campaign. As I understand it, Shadow has the group, not individual characters, have levels with every session as an adventure and leveling at the end each one. (If I'm wrong, sorry)
One of the things that I didn't care for in first and second addition Dungeons and Dragons was that every class had its own experience chart. It made the bookkeeping more confusing and it also created a real disparity between classes. Yeah, becoming a high level wizard really was an impressive thing to pull off but, considering the years of frustration that it took to do it, small wonder so many high-level wizards in any given setting were insane and evil.
One of the many things that I really liked about third edition was how everyone just shared the same experience chart. In part of how they did that was by also leveling the power disparity of classes. And while I did have a lot of fun with fourth edition, I do think that they went too far leveling the playing field there.
However, the real appeal in milestone advancement is narrative. Gaining a level becomes a natural part of the story. You don't learn new spells or new sword techniques in the middle of a fight, not unless you're in something like Dragonball Z. Gaining a level becomes a reward for accomplishing something, as oppose to a reward for grinding.
And, as I have grown older, the narrative part of role playing games has become more important to me. You can blame those indie games.
I do realize that there are some systems milestones won't work with. The original TSR Marvel system uses karma for advancement and for bennies. It's a game where you spend those points in the middle of a fight to do something new. But that system has incremental advances as oppose to a big level.
When I first heard of milestone advancement, it completely through me off. It wasn't what I was used to, it wasn't the paradigm I had grown accustomed to. However, in practice, it makes perfect sense.P