I was curious about the Sunfire 600x2 amp, so I found the user manual. This is what it states about the standard "voltage drive" vs. the more tube-like "current drive" (emphasis added):

------
I've included two kinds of left and right outputs:
(1) a standard voltage-source (i.e., near zero impedance) output for all typical applications and:
(2) a higher-impedance current-source output, which many prefer for electrostatic, planar magnetic, or ribbon speakers. Or you can biwire your system with the voltage source driving the woofer(s) and the current source driving the upper part of the system. In many cases this provides by far the best possible in ter face between the amplifier and the speaker system.

Whichever way you decide to hook up the Sunfire power amplifier, it will create a multilayered sound stage that is deep, wide, three-dimensional, and utterly believable. The optional current-source output can coax forth a sensuous, delicately detailed musical voice long associated with low-powered classic tube amplifiers. (The current-source characteristic of vacuum tubes is the dominant factor in the sound stage delivery of classic tube amplifiers.)

[snip]

NOTE: The Current Source output is a Voltage Source modified to yield a Current Source impedance of one ohm. This corresponds approximately to a vaccum tube amplifier output impedance and constitutes the dominant factor in the soundstage delivery of classic vaccum tube power amplifiers.
-----

So the Current Source output utilizes an artificially high output impedance -- most solid state amps are in the 0.0X ohm region -- to mimic the voltage fluctuations tube amps produce when connected to your average speaker. (Naturally, these fluctuations alter a speaker's frequency response, which is the source of "tubey" sound.)

While researching this stuff, I found a detailed article that talks about the role output resistance plays in how an amp sounds. It's an interesting read.