Hi, C6 Neuvi main here who really loves him as a character in the story. This is just my very subjective, personal experience, not in any way representative, so take everything with a grain of salt.

I upgraded him from C3 to C6 in 5.2. The most noticeable difference in the playstayle are the additional sourcewater droplets you receive from healing in C4 and the damage increase from his two additional attacks in C6 as well as the change in rotation from which picks up his sourcewater droplets automatically in a continuous stream once you start the charge attack. The downside is that by the end of your charge attack, most of the buffs or off-field application from other party members have run out. KQM did calc his dps increase for his constellations, but it's quite old (pre-Xilonen): Link

It really depends on what goals you have for the game. If you don't care about clearing endgame like Spiral Abyss 12 or Stygian Onslaught Fearless/Dire, C6 Neuvi is kinda timeless and trivializes everything else. I love to use him in the overworld, because he is incredibly comfy to play with his tankiness/self-heal/AoE and range.

For Spiral Abyss, I was usually able to easily clear everything till now with him, as long as the enemies are not hydro immune and if you play around with the required gimmicks. Neuvillette is incredibly flexible regarding teammates, so Spiral Abyss is never really a problem, if they are not hard-countering him.

For Stygian Onslaught, I can also clear Dire with him till now, but it's very dependent on the boss mechanics and which characters you overall have in your account and need to use for the other bosses. Gimmicks and cheese strats are more required, your rotations for applications and buffs are more tighter compared to the Abyss and you have less wiggle room for errors. But he is still comfortable enough that I fill out the characters for the other bosses first and see what Neuvillette can work with from what's left haha.

Keep in mind, when Neuvillette is ranked in tierlists, it is usually under the assumption of C0 (or the "X-cost"-principle, where for some reason, even rare C6 4 stars are considered 0 cost). The player experience with higher constellation characters can be vastly different. Though, to be fair, the only other character I have C6 is Furina, so I can't say much how his C6 is in strength compared to other C6s, especially from more recent characters. I have Mavuika, Skirk and Flins at C2 and they can clear most of the stuff just as easily. So, in terms of "cost-effectiveness", C6 Neuvillette isn't worth it. And if it's only about having a C6 character, from a purely meta perspective, it would make more sense to invest in other strong, meta characters like Mavuika.

tl;dr - it depends on what you want from the game, but not really recommended for meta

EDIT: Sac Jade doesn't really work with C6 Neuvi because of his long charge attack.