I find I prefer alternate modes to a sandbox version of the game, with a few exceptions.
When I finished Ender Lilies, I couldn't find the motivation to finish a New Game+; it's just the same map with all your abilities already unlocked. The potential to easily sequence break didn't appeal to me.
What did get me obsessed for a while was the boss rush mode. I loved having the opportunity to use all the tools at my disposal to optimize my combat strategy and overall time. The combination of a clear goal and an unlimited toolkit carried my interest for many more hours.
I didn't finish the New Game+ mode for Parasite Eve either, even though I'm aware it's the only way to achieve the true ending. Again, there's too much repetition of the same content. What's unique to my experience with this game is the added motivation to do the dreaded thing: grinding.
I didn't know this until I was nearly done with my first playthrough but the garbage that you pick up after random encounters can be traded in for powerful weapons after collecting 300 pieces IIRC. The first weapon I traded for was a shotgun and that thing is godly. The best place to grind for trash is the first floor of the Chrysler Building because there are so many crows that spawn during a single encounter. The thing is, I was supposed to just use Aya's thief ability and not actually kill them because killing them drastically reduces their encounter rate.
Guess which big dummy didn't know that and killed them?
The exception to the rule and my favorite version of end-game content to this day is the New Game+ mode for Muramasa: Rebirth. For those not in the know, Rebirth has four DLC characters and their stories added to the base game. Like the main two characters, DLC characters are restricted to specific areas of the map, certain challenges, and story-related bosses. But once you've finished everyone's stories? The entire map is unlocked for every character. You can now bring any character into combat encounters they couldn't access before and experience old battles with new move sets. The ability to do this with all six characters adds so much more content and I love every second of it!