So what you're are really asking is, hypothetically, if all things were equal, and they were in the same tank, who would live, and who wouldn't?
My guess is similar to the above, the dovii (unless it knew better (maybe because of the shrimps threatening color)), would stay away, or if it didn't, would try to eat the shrimp, but...
If the shrimp was on it, it would break the dovii's jaw with one quick snap, and in the end, the dovii would probably limp off and die.
The reason I say this is, the speed of a mantis shrimp hit, is as fast as a .22 bullet, and can crack aquarium glass. The hit tends to vaporize surrounding water, and creates a flash of light.
This may be why, one of the nicknames for mantis shrimp, is thumb splitter.