Generally asan+msan detect more errors, and some quite significant ones. For design reasons, valgrind cannot detect most stack oob bugs. The only issue with msan is that it's a bit trickier to use, particularly if you have lots of dependencies.

Both approaches have their right to exist, but I have been preaching to people that valgrind does not find all memory safety bugs that modern tools can find, and they should be testing with sanitizers. I still experience that many people are not aware of asan+co and only know valgrind.