I have used both quite a bit and found good success with either.
I have found that if you use the tape, the crows respond extremely well....but, most tapes imitate multiple birds and when the crows come in, they come expecting to see a fight with an owl or a carcass or something. If they come in and don't see any other birds, they take off really quickly. They are an incredibly smart bird.
I have found that they are more forgiving when using a mouth call because they come in looking for one bird. This has just been my experience. I am certainly not an expert on the matter.
Either way, crows respond exceptionally well to calling and are a great bird to practice wingshooting on.
have fun!