I know retagging question using Retag questions privilege doesn't give you any reputation and also doesn't require peer review. On the contrary, using edit for retagging with a minor change in the content of respective question gives +2 rep(unless the rep cap is reached) if it's accepted and also requires peer review which ensures correct/useful retagging. Frankly speaking, this fact encourages me using edit instead of retag question privilege which may be true for many other users, IMO.
So, which method should I use for retagging?
If I edit the question I get a peer check to make sure my re-tagging is acceptable.
I think my retagging may always not be perfect which is not checked if I use Retag privilege but, if I use edit then a safety check is ensured via peer review which encourages me to use edit.