There has been quite a bit of discussion on this in the forums. You can likely find some of it by searching on appropriate terms in combination (e.g., paper, engrave, vector cut).
Both approaches are workable. Vector cutting is faster. Engraving can create finer detail.
You can adjust for the problem of blowing bits of paper with a work hold-down solution like a Seklema Mat from Johnson Plastics or, a piece of draft board or other flat, even heavy stock coated with repositionable adhesive (available as a spray).
Depending on your design, there are potentially issues with overburn of corners and sharp turns in vector cuts. Solutions for that have also been discussed at length here and, include creating lead-ins and outs, rounding features in your design, etc.