I'm not convinced the two are mutually exclusive. As evidence, during periods where I have actually had various tikun olam-type volunteer commitments of sorts, whenever they would overlap with my usual davening time, I would simply arrange to pray by myself earlier or later. I never had a time where I could not volunteer because I had to pray or vice-versa. That said, I wholeheartedly agree - fixed acts of tikun olam in some form are definitely as essential as fixed time to daven, if not more.
Russia: U.S. plan to provide air cover for Syrian rebels undermines Damascus fight on ISIS (Reuters)
from the article: Jews pray too much