I use both, but not in the same tank.
I've used Caulerpa for 3 years in my fuge under by 210 - it's lit 24 hours a day. Never had a problem with it and it grows really fast.
I use Chaeto in my fuges under both my 125s - they're lit on the opposite cycle of the tanks. I've had more issues with this - getting caught in the power heads, being touchy with lighting, etc.