Both doll bodies are made of plastic, and both heads are made of the same soft, squishy plastic Barbie heads are made of. However, the two are quite different. Here are the pros and cons of both:
VOLKS
Pros: Detailed bodies, anatomically correct, great anime-style heads.
Cons: Less choices for heads and bodies, more expensive.
OBITSU
Pros: Detailed bodies, anatomically correct, lots of choices, cheaper.
Cons: Not-so-great anime-style heads.
Personally, I've always been a Volks person. But if you want to try Obitsu, that's fine, too. To buy Volks supplies, visit Tenshi no Sumika. For Obitsu supplies, you should go to The Junky Spot.
NOTE: Volks dolls are also known as Dollfie dolls.