More fun as in I enjoyed the weapons I picked for my two chars as more enjoyable to use. I never level beyond 120, not really because of the meta, but just because I don't enjoy being too powerful or a jack of all trades. I prefer specialized builds.

If you don't care about online play or a special build, you can just lvl up to your heart's content. Get platinum, try all the weapons etc. It all comes down to what you want to experience: do you want to test new weapons? do you want to push the difficulty by progressing through ng+ games? do you want to try online play, either co-op or invade? Maybe you want another challenge, like a BL4 run.

If you just want to "complete the whole game" it's easiest to do with a levelled char in ng+. If you want to experience the thrill of exploring new areas, maybe you shouldn't be too strong. It's hard to give a definitive answer tbh.

You should treat yourself to the DLC tho. It's very, very good and it has the most interesting/fun weapons in the game IMO.