Barron was a highly mobile, offensive orientated defenceman in junior that made him a valued prospect. like many prospects, his development, once drafted, has definitely plateaued.
Barron is still possesses above average skating ability, has good offensive vision ( look at how many goals he scored in limited playing time) which allows him to both initiate and support offensive rushes, he walks the offensive blueline well using his good agility and puck handling skills and possesses a surprisingly good shot. It's defensively where Barron's game has considerable holes. His defensive acumen is suspect as Barron makes poor reads, does not really have/maintain good gap control and, despite his size, lacks the strength to control opposing forwards along the board or to box them out in front of his net. Barron, like many young defencemen, is very susceptible to a heavy forecheck and when pressed, he makes poor plays that places his team in trouble in the defensive zone. When forechecked, Barron has an unfortunate 'deer in the headlights' look. After watching him play a few games, you will know what I mean.
As a Montreal fan, I never like trading away skating ability and Barron is a better skater than Carrier. Barron is also bigger, younger and far less expensive than Carrier. While the trade may favour Montreal this year, it may not be the same over the following years if Barron's defensive game ticks up a notch. That is, of course, the big 'if' in this transaction. From Nashville's perspective, this is a bit of a swing for the fences trade. Barron will score goals for you. The question will be if his defensive lapses will cause more goals against.
As I said, you trade away skating ability at your team's peril.