Bushnell: more consistent quality on the glass, stronger scope body, heavier, has their water resistant coating
Burris: has a superior semi-turret style adjustment instead of Bushnell's simple finger adjust, usually lighter, can have the ballistic plex reticle,which is nice for long range
I would add that the Bushnell 4200 3-9x40 (if you can find them anymore) is a hybrid 3200/4200 that will be similar in price to, but will have better glass than, the 3200 3-9x40. It uses 4200 glass with 3200 adjustments, which is why the price difference is so small.
The Vortex diamondback has much better adjustments (a semi-target turret) and a better warranty, but the glass is inferior to the 4200 (but similar to the fullfield II or 3200).
You might also consider the Nikon Buckmaster 3-9x 40mm in the same price range. It has the best turret design for long range (adjustable to zero) and most consistent adjustments in that price range,IMHO.