Whether you choose BM or ME, your decision should be based on the duties and responsibilities of that rate. You could request a TACLET billet, and then get a cutter on the Great Lakes. You can ask for palm trees and get penguins. Needs of the service always come first. Keep in mind, you probably would not be able to do TACLET teams your entire career; as it is a unit comprised of billets that you have to compete for, just like every other unit. In short, do not choose a rate just because of one billet at a particular unit. The Assignment Officers (AOs) are always saying, keep your dream sheets diverse.
I don't know about ME, but the BM rating requires sea time for advancement. And if you want to be competitive, that might mean a lot of sea time. BM is a sea-going rate and you will have to go to sea, to gain sea time. Sea time means ships. Some BMs go on buoy tenders and construction tenders and do ATON their whole careers. Some BMs do white hulls and stations. BM is a very diverse rate and only a small percentage of BM billets are at TACTLETs.
I'm not saying, don't do it. What I am saying is, be familiar with all of the units BMs can go to, which is almost every unit in the Coast Guard. Be realistic about what you are getting into and do it for the right reasons.