Contrary to other reports I find a standard OBH-11 with an OBH-2 power supply indistinguishable from the OBH-11se. The comparison was only a couple of days since the OBH-11se was borrowed. I do not find the OBH-11 to be bass shy even compared to my McCormack MID. In fact I find the OBH-11 to be very balanced in its frequency presentation. However these observations are most likely colored by my preferences and as always your mileage may vary.
I have both...it's really close...IMHO, it is not worth the cost difference...also, I agree that a big portion of the difference comes from the power supply, but I don't think you can get that by itself...if you can, that would be the best...but remember, I'm a tube guy, so I don't like either of these very much (too grainy).
You can buy the power supply separately (OBH-2). I bought mine from Stone Audio since it was cheaper than from US sources. It is a significantly larger unit and is a regulated supply. Actually someone on Audiogon was selling a standard OBH-11 with an OBH-2 power supply for $200, which is not a bad price (No it is not me! )