I would say move over to the enhanced version, that is unless you are near the end, so you could have a complete original playthrough, and maybe do an enhanced with a different character, or even a new game plus.
I don't know the difference of graphics, so maybe do a test run of an episode for comparison to see if there is a large leap, where you could make it worth a restart, or that it could distract to have the sudden change.
If you like the idea of like the future games thing, I would say that should especially be a deciding factor in starting over if you plan to play the other games in leading up to Borderlands 3 coming out. Might give you something to talk about to if you have experience with the differences and later games.
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Through dream I travel, at lantern's call
To consume the flames of a kingdom's fall