I would like whatever technical advice or opinions you can provide on the three scopes listed above.  I am leaning toward the Bushnell 3200 but would like to know the pro's and con's of each model before purchasing.  Thanks for any help you can provide.  

The Leupold VXI (and VXII) are two piece tubes...but otherwise the quality is there. Great warrantee from an outstanding company.
I own two 3-9x40's and have had zero issues. For a few bucks more you can step up to the VXII lineup.
IF you're looking at the lower end Leupolds, also check out the revamped Redfield line-up. Make by Leupold and great bargain for the price.

The Burris Fullfield II is a one piece tube. My Fullfield II 3-9x40 is comprable in clarity to my VXI's. Seems to do better in low light than the VXI.
This is my "go to" scope on my "go to" woods gun, a Model 70 in .270. Been on the gun two years with a TON of use, and still holds true.
Have heard some horror stories the past year-ish of quality control issues, though.

Bushnell 3200...only one I own is the 10x40 Mil-Dot.
Durable, decent glass. Comes standard on some Barret's so it's obviously stout.
The only other two bushnell products I have owned were cheap (Under $100) and weren't very good, IMHO. Cannot comment on customer service.

(If I were buying, based on my own experiences, I'd rank them just how I outlined them in this post...JMHO).

I have had both those scopes (Leupold VXI and Burris Fullfield II) and really liked them both.  I let a friend talk me out of the Burris and he put it on his WIn 70 300 mag and he loves it.    I put the VX I on a FAL and it is holding up well.  We put them side by side and could not see a lot of different between the two in the early evening.  We did not try later though right at dusk to see which would give us the best light.  

I recently came across another scope that I truly like, a Nikon Buckmaster.  I tried the Nikon Buckmaster after the Nikon Prostaff I bought for the muzzleloader has held up exceptionally well and the impact has not moved noticably after 3 years of hunting and shooting at the range with it.  The Nikon is not mounted at the momen as I sold the rifle it was mounted to but I believe it is every bit the scope the Leupold and Burris are.  On Bushnell, I had a Bushnell scope about ten years ago that had a drifting zero, I know I just had a lemon but I have not purchased a Bushnell since.  My father has a Bushnell on his 300 Win mag that has been on it many years and he loves it, so they are good scopes as well just not a lot of personal experience with them.

Overall I believe their quality are very similar.  With warranty, a coworker was given an old leupold that was broken a couple of years ago from the 70s.  He took a chance and sent it in to Leupold to see if they would fix it.  They did promptly and he placed it on his deer rifle.  On warranty I would give the edge to Leupold.

FFII has 95% light transmission.

Bushnell 3200, Nikon buckmaster, Leupold vx1 all have around 91%.  If you are planning on using this as a hunting scope or other low light applications the burris is a better buy IMO.

For the record I own all the scopes listed above except the nikon.  They all have pros and cons but the burris is my favorite.

ETA: If you can expand your budget by just a little the Elite 4200 in a 3-9 can be found for just over $200.  They have 95% LT and glass that will blow away any of the other scopes listed in this thread.  IMO its the best buy 3-9x40 there is- period.  4200 linky