5th Edition: I've run several fifth edition games to levels 15+. 5th edition characters require about the same amount of experience for each level, making leveling very consistent. Characters will reach 2nd level after one session, and third level by their third session. After that they will level about every 3 sessions. Many, many fifth edition players remove player motivation and use milestone experience to control the rate of advancement.
5th edition characters do not stop increasing in personal power. The curve is more suited to a B/X style game, but the endless gain of personal power provides a very different endgame.
For an example, my ex-wife played a barbarian during Horde of the Dragon Queen. Her standard procedure after level 10 was to jump to reach whatever dragon was flying nearby and grapple it while hitting it with her axe several times each round until it died. Once a dragon lived through two rounds of this. At the end of the campaign, she had upwards of over 300 hit points, and during her endless rage only took half damage from anything but psychic attacks. Not counting healing or other defenses, this generally required doing 700+ points of damage before she even felt threatened in combat. Considering the bard could heal everyone for hundreds of hit points every round, it often required many hundreds more points of damage.
Our battlemaster fighter wore heavy armor that provided damage reduction. I could only manage to hit him, with anything but the most powerful monsters, 5% of the time. Since he also had the lucky feat, he could nullify 3 of those hits every game session. He also had over 100 hit points.
Do you know how many times you have to attack a person before you hit with a 20? A lot. The fact that the first 3 important hits could be waved away with lucky made him almost invulnerable.
High level 5th edition play, with its focus on constantly and steadily increasing personal power feels very anime, very Final Fantasy. Everything is very elastic, you're up, you're down, the power levels are very high, and the threat to the characters is very low. Combat runs amazingly quickly, considering the complexity of the game. It's extremely well designed. Often the most time consuming part of combat is doing three column subtraction of hit points.