Would a Federation warship like the Defiant out gun a Star Wars Star Destroyer? Who has a bigger armada? Who has the tactical advantage? Don’t forget that The Federation includes the Klingons, who love warfare and have fast, agile, heavily armed ships, with cloaking devices, and the Vulcans with superior logic and tactical planning.
Yes, shields normally let transporters pass right through and definitely need to be specifically configured to block transporter beams. That’s why no away team has ever been stranded because their ship had to raise shields.