First, it's just fun when both leagues' finals are on alternating nights.
NHL is awesome how anything can happen at any time and each goal becomes a game-changer. It was CRAZY yesterday when Chicago tied things up late in the 3rd with some beautiful teamwork and passing, only to have Tampa take advantage of a sleepy 4th line and score the game winner just 13 seconds later. I have no vested interest in the teams this year, so that dampens the fervor some, but it's still fun to watch. Also, much better if you can find a CBC feed. Their Canadians are just better than NBC's Canadians.
I have no real ties to the NBA finals either, but I wouldn't mind seeing the Warriors win after Kerr came to Seahawks camp to get some pointers from Pete. It's almost like Carroll's coaching tree reaching back across sports. He got so much inspiration from John Wooden, whose books drove Pete toward NCAA and NFL championships, there would be a nice symmetry to him giving back in a sense and influencing a basketball coach toward a championship.
But if LeBron can will his Cavs to the title, that would be a great story too. I'd be happy for the people of Cleveland to finally have a banner in the rafters.