I’ve seen the show a dozen times, and I personally can’t tell if I prefer one side over the other. Whichever side you chose, I’d sit in the box closest to the back of the theater. You’ll want to chose the seat(s) also towards the back of the theatre inside the box, as you have to lean forward the least.
When it comes to the mezzanine/dress circle boxes, those should offer better sight lines as you’re not staring straight down, but those are more expensive.
I actually thoroughly enjoyed my balcony box experience, I was sitting house right. You do stare straight down, but you’re in super close proximity to the stage and can see all the lights and effects from awesome new angles. The majority of scenes are played center stage. The only thing you may miss is the fireplace on the back wall.