The Browning optical coatings are the same, but the Brownings lack the Bushy's Rainguard moisture repellent lens coating.
Of the two that you listed the 3200 is a bit better scope. But for the same money you can pick up a Nikon Team Primos 3-9x40
from SWFA. The Team Primos are rebadged Monarch UCC and feature the same quality glass and coating found in current Monarchs. It's a much better scope than either of those on the OP's list, and much better than a Burris Fullfield II. Nikon Monarchs and Leupolds have transferable lifetime warranties if purchased as new. Bushnell is I believe lifetime of the original owner.