I have never heard of the Bis, but we have the Quadrafire and love it. We have had it installed for about a year and a half, no service issues other than a knob that broke and was replaced immediately. The person who sold us our fireplace was a friend of a friend and she very highly recommended this over other options, so we trusted her knowledge and experience and have not been disappointed.
Kim

I have the BIS tradition CE. It is a smaller version. Works great and gives off tons of heat.

I can load it up at night about 10:30pm (3 good sized logs) lower the air damper and at 7:00am I still have a good set of hot coals going...throw another set of logs on and I'm good to go.

both are fantastic. Pick your poison.
I have had no problems with the 7100, (from a dealer standpoint)
I dont sell BIS, but there a great manufacture.
I burn a 7100 in the showroom, and it will blow you out if your space isnt large enough.
I get 12-13 hour burn times with a packed firebox and good air control on the 7100. I get about 8 hours with it full open.

I have a Qudrafire 7100. Bought it Oct. 2010. I'm using mine this winter. The burn time for 16 hrs is when you have dampered all the way down (less then 10 btu.). When i have mine going, it's on the highest setting. My wood will last 3 hrs. top. I don't now how it is a effiecient fireplace. If anyone is getting 8 hrs. burn time on the wood, they are counting the hot coals as they run out of burn time. Maybe i have bugs to work out yet, i don't think so. Good luck everyone. Mike