Well, in case you don't get any responses, I'll give you my "limited" experience, (which albeit is only somewhat relevant, as it was not a direct comparison, and it was separated by a few years). So take this with however many grains of salt you want!
My friend has owned both the BAT 150 (non-SE version though), and he extensively auditioned (for a few days in his system), the VAC 300 (the original version, not the 300.1 version). I got to hear both in his system, so you're going to be getting my limited, but first hand, experience with both.
The BAT 150 was a very good amp. It soundstaged and imaged very well and the tonal balance was very nice. However, it was not quite powerful enough in the bass region to get my friends speakers, (the Avalon Eidolons) to really come to life. My friend eventually replaced it with the VTL MB-450s, which did have the power to drive the woofers on his Eidolons in the manner that really brought the bass response up to snuff. However, the BAT amp did have plenty of power reserves, as we could not get it to clip, (something which we did manage to do with the Manley Neoclassic 250 that we directly auditioned with the BAT 150). If I was to grade this amp, in my friend's system, I would give it a solid B+. (The VTL MB-450s would get an A-, due to it being more powerful, and hence a better fit for the Eidolons.)
Now, my friend eventually upgraded his speakers to the Rockport Antares, which are an even more demanding speaker than the Eidolons, as the woofer is bigger (a 13" vs. 11"). My friend also by this time had upgraded his amps to the Lamm M2.2, a 220 wpc hybrid amp, which is one of the two best amps I have heard. The other amp that ties the M2.2 is the VAC 300. Both have different strengths and weaknesses. The Lamm M2.2 has an iron fist when it comes to bass response, and it has great imaging and soundstaging. The mid-range is fairly neutral, with just a touch of tube sound to it. The treble is very, very good, and the best I had ever heard, even better than the legendary DarTZeel NHB 108, which my friend tried too. (Well, it was the best up until I heard the VAC 300). The VAC has incredible treble response, well extended, light, delicate and airy. I have never heard better. The mid-range has more tube sound than the M2.2, and is not quite as neutral, but when listening to vocals, you'll not care one whit about that, as you'll just sit back and enjoy the music. The imaging and soundstaging is also great, and the equal to the M2.2s. However, its weakness is that it was a bit weaker in the bass response than the M2.2s. In addition, the initial attack on percussive instruments, (drums, piano, etc.) seemed just a bit slower than on the M2.2s. (My friend had to make a difficult choice between the two, and in the end he ended up sticking with the M2.2s, although even he admitted that it was a very close call. In fact, he said that he would have loved to own both and use the VAC for vocal types of music, and the Lamms for classical music, but financial constraints prohibited that.) I would like to point out that I am being VERY picayune about this, as both the VAC 300 and the Lamm M2.2s are easily the best two amps I have ever heard. If I was to grade the VAC, I'd give it an A, (despite its minor shortcomings), as I would the Lamm M2.2s - Hey, a tie!)
My recommendation would be to get the VAC 300.1.
One caveat regarding the VAC 300 though: They get hot. They can easily raise the temperature in your listening room by several degrees, (whereas the Lamms will raise the temperature by a few degrees, as they run very warm themselves.)
PS I was told by one VAC 300.1 owner that if one can afford to buy a second 300.1, and bridge them up to 300 wpc, (which he was doing), that the bass response can be brought up to the same level as the Lamm M2.2s. (This is second hand knowledge, but I would tend to believe it.) My problem with doing that would be the heat generated by two amps would be very problematic, especially for any room without air conditioning.
Good Luck in your search.
