I would say it really depends on your skill level. If, like me, you're a relatively weak player, playing lots of "easy" and "medium" puzzles is probably more beneficial. You want to train yourself to recognize patterns and interactions that are likely to come up in a game. In that case, seeing lots of different tactics is probably best.
As you get stronger, the basic tactics from "easy" and "medium" puzzles will be almost always seen by both players (you still need to recognize them because if you miss your opponents simple fork, you're going to have a bad time). Focusing on harder puzzles will help you find those more complex patterns and tactics in your games. In this case, both lots of tactics and complete understanding of every puzzle is probably the desired outcome.
I've listened to GMs talk about puzzles where they look at it for hours and when they have a "solution" they still don't actually know if it's solved until they consult an engine, the puzzle creator, or their coach. (Compared to a simple forced mate in X puzzle).
Additionally, it's all about where your strengths and weaknesses are. If you're really good at a particular type of tactic, de-prioritize continued training of that tactic and focus instead on your weaknesses.
Most people have a bias where they would rather do 5 puzzles they're good at and 1 they're bad at, which is fine if you're doing it purely for entertainment, but if you're trying to improve, reverse the ratio.