I have played every version from AD&D to 4E, including some spinoffs like Pathfinder (our current implentation of choice). The fantasy realms that these systems allowed our DM to create and us to fill were always lands of grand destinies and heroric quests. However, often times as we worked our way up the level chart, things began to get less and less epic and simply "better."
The feeling of one's character becoming more epic was always a core need of mine for D&D. I remember spending hours and hours looking over spell lists for my wizard, trying to find the most awesome thing I could add to his spellbook over the course of the next few levels. Remember the thrill of casting Fireball for the first time? This applied to other classes too, of course. Getting that second attack as a fighter, or finally being able to blast an army of undead as a cleric were truely great moment.
With the later editions of D&D, much of the feeling of becoming more EPIC at higher levels was replaced with simply getting "better." No real new talents are unlocked, you simply are better at doing what you've been doing. This was especially bad in 4E, where the vast, vast majority of powers at higher levels were simply tweaked versions of what you had at lower levels.
With 5E I really hope the designers swing back towards the epic feeling of level progression. I want my characters to become awesome pillars of might in the their respective areas, not just better version of what they started out as.