I run two campaigns and decided to run them differently based on the PC desires. In the combat-heavy war-torn campaign I expend all points except those over the leveling up threshold to make it longer and tougher thereby giving the players more combat. The narrative heavy campaign I have been maintaining the accumulation of all XP so as to make it more fun because they wanted to find items and combat isn't such a high priority. Both groups have decided they want to join forces and create a single campaign but I can't until I can make them close to equals so I wondered which version is the correct ruling.
XP continues to stack.
PHB 12 states,
Also record your experience points. A 1st-level character has 0 XP. A higher-level character typically begins with the minimum amount of XP required to reach that level (see “Beyond 1st Level” later in this chapter).
If XP reset after each level, then a 1st-level character and a higher level character would both start with 0 XP.
You might have noticed that under this system, the XP curve is a little weird because characters level up a lot faster after level 10. However, this is intentional (from a designer tweet):
it's an intentional bump - higher levels are meant to move a little faster than first 10
There's some more discussion of this issue at this question.