I’ve seen both as stage productions, but not as movies. (Actually, I was in JCS…TWICE

). At the time, I saw nothing problematic, but in retrosepct, I can see why some people like to stay away from them.
A lot of it depends upon who is putting it on. Both times I was in JCS, we inserted our own Resurrection scene at the end. We tried to make it as Catholic as possible. But then there was one of my fellow cast-mates who saw a production of JCS that ended with Judas, Jesus, and Mary Magdelene all getting on a motorcycle and driving off together!
Godspell I’m not as familiar with as it’s been a number of years since I saw it.
Again, as with any stage production, there is often an opportunity for great leeway in certain areas. The text is set, but the background, costumes, and the way lines are delivered are unique from show to show. Thus, it can be very different depending upon who is putting it on.
They’re certainly not the best depictions of Jesus’s life, but they’re certainly not the worst, either.