Look at Dallas vs Edmonton last year. Arguably the 3 legit contenders in the west were Dallas, Vegas, Colorado. Dallas played both of them and then looked like a corpse in rd 3. Meanwhile Edmonton got their usual 1st rd bye and then got to play a shit Vancouver team who was using a 3rd string goalie. They got to come in fresh after a very easy first two rounds compared to Dallas, and it showed.
So there is something to be said for a team getting it done on the weak side of the bracket, while another team does the dirty work on the other side.
I don't see a scenario that extreme this year, since Dallas/Colorado only have to worry about each other until a potential WCF vs Vegas. And Tampa/Florida shouldn't have much to worry about besides each other. But the thing is, both of those matchups will be war, and will wear down the winner enough that it could affect their next round.