Looking to upgrade pre amp and looking for suggestions

The BAT 51se would be a HUGE step up! 
I think you'd be blown away by the improvement. 

Good luck 

I would think that it would depend on what you are looking for sonically.

Of those that you mention, I've owned the BAT VK-51SE and the ARC Ref 3. I've also had the VK-32SE in my system for an extended audition.

The BAT VK-51SE and the ARC Ref 3 are both very good preamps, but very different sounding. The BAT being more powerful and dynamic, possibly the best bass of any preamp I've heard. The ARC Ref 3 offers higher resolution and a more extended top end with more detail.
I didn't care for the VK-32SE, it had more midrange bloom and sweetness than the 51SE, but at the expense of dynamics and power.

Another tube unit you may consider is and Atma-Sphere MP3 or MP1.

As for SS, the only preamp that would interest me is a Klyne 7 series.