Personally, I don't think it's the setting as such that matters. It seems to me to be more about the performances themselves and the overall production styles and standards. I mentioned the June Tabor concert at St. Luke's, which I thought was wonderful. Looking back at that, what made it so good (IMHO) were:

1. The superb performance by June Tabor herself
2. The excellent musicians performing alongside here
3. The choice of material
4. The simplicity of the setting
5. The quality of the sound and camera work

Interestingly, I also absolutely loved the Springsteen Seeger Sessions concert at St. Luke's. If I remember correctly, there were 16 musicians playing on stage - many of them on a variety of instruments - and the overall atmosphere and production was stunning. I then saw a concert of the same things by Springsteen in the open air in Dublin - and it was just as good!

So, my summing-up would be that it's not so much the setting as a combination of things that make the occasion work.