BAT Pre Amps

Will I hear a big difference between a BAT 3xiSE and BATs 31SE and 51SE? If so what will be the difference. I have the 3Xi coupled with the Bat250SE and Montana ESP2 speakers.
yes. I had a 50SE years ago that I upgraded to 51SE. In the interim my dealer loaned me a 30SE (may have been a 31SE). Anyway, both the 50SE and the 51SE surpassed it. More weight to the notes and just more there there. It was not subtle.

Your 3Xi is a great pre...but BAT has better. Used 51SE's are a pretty good deal....
You should be able to get a used 51SE for about $2,600-$2,700 today with moderately new tubes (less than 500 hours max and 90%+ life remaining).

The 51SE is definately going to provide an upgrade over the 3xi you are currently running and the difference in price between the 31SE and 51SE is tiny (a few hundred dollars at the most), making the 51SE a lot more logical.

I recently bought a new preamp (this week), the 51SE was on my short list. I was offered one at $2,700 (seller came right out on my first contact that he would lower the price to that level) including shipping about 2-3 weeks ago - but I decided not to go that route.

Having owned BAT preamps and amps in the past, the one thing I never liked was how quickly their products lost value.
Be aware that the 50SE/51SE are fully balanced only on both the inputs and outputs. If your sources and amps do not have xlr connections, you would need to buy adaptors as well. However, the 51SE at the above mentioned price would be a great deal and the cost of adaptors is not too great. I have not owned the pre you now own, but had the VK 5i as well as the 31SE. The 31 SE was much more dynamic and immediate sounding. I eventually settled on the VK31 to have the ability to roll tubes. Hope this helps.