I guess I would classify any amp that struggles to provide gobs of current along with any voltage it is able to pass, as the type of amp you're referring to. I've heard those and they can be impressive, no doubt. But there's something about the presentation of an amp that can deliver huge amounts of current, even into 4 or 8 ohms loads, that makes the bass just sound nicer. This must be a control thing. Now I know there are amps that can swing impressive amounts of both voltage and current equally, but most put a priority on one or the other. I would agree, 120v in the vehicle and we would certainly be using higher impedance drivers. Not many home setups getting anywhere near the 2ohm territory. But regardless of the starting voltage, I just prefer the presentation of a current source amplifier over a voltage source. If you read some of the Bob Carver white papers on some of his magnetic (or whatever) amplifiers, he touches on some of that and why this is the case. He also offers voltage source and current source taps on the back of some of his amps for this reason but you will have to partner speakers wisely with those. Planars like Magnepans would like the current source taps but high sensitivity drivers like a Lowther would prefer the voltage source taps. Low sensitivity, low frequency drivers are likely to do better on the current source taps; where higher sensitivity midbass and midrange drivers are likely to do better on the voltage source taps.How many high voltage amps have you auditioned? Really the only benefit of high current is that we're starting with only 12V at the power supply. Were our cars to use a 120V generator I think 8 ohm drivers would be a lot more prevalent.
I remember the first time I came across this difference, when I had a measly little Soundstream Reference 300 and I kept blowing the fuse when using the 'high voltage' setting. I reluctantly flipped the switch over to 'high current' and scoffed at the idea that I had to settle for lower power but I didn't actually notice a big difference in output. What I did notice is that the bass was actually smoother and deeper. It just sounded better to me. The final load presented to the amp does have a lot to do with this but when the combination is right, a gain in subjective performance can sometimes be appreciated. But again, I would think this is mostly a preference thing.
