The med school route involves two separate routes. The most direct (and most competitive) route involves 4 years of med school and then 6 years of integrated plastic surgery residency. This residency is THE MOST COMPETITIVE residency to match into. Board scores for matched residents fall in the 99% of test takers on the USMLE. Other routes involve doing some sort of surgical residency (general surgery, ENT, ob/gyn, and urology) and then completing a 3 year plastics fellowship. As you can imagine, these fellowships are also VERY competitive.
The dental route involves 4 years of dental school and then a 6 year OMFS residency. You must do the 6 year residency (that includes 2 years of med school) to be eligible for plastics fellowships. After your OMFS residency, you can apply for plastics fellowships. I believe there are many fellowships that aren't accredited by the same institution as the med school residencies, but this doesn't necessarily mean they put out incompetent clinicians.
I personally think the route to plastics through dentistry seems like a roundabout way to get there that isn't really guaranteed. Matching OMFS is said to be just as difficult as matching PRS in terms of competitiveness. Also, going through dental school to do only facial plastics seems like a waste. IMO, you should pick whichever field you would be happy in if you DIDN'T match plastics (which is most likely to happen). If you could see yourself practicing as a plain OMFS or a general dentist, go dental school. If you would rather be a physician, go to med school.