Thiel Owners

My understanding is a faster slew rate for a given component is better -- up to a point at which little-to-no difference is heard.  Musical transients are only so fast, and if the component is substantially faster than the fastest musical transients, generally straightforward to do these days, you're good.  That's not to say within the component you don't need much faster slew rates, like the I/V converter after the DAC chip.  Sort of like high-frequency response and harmonic distortion.  Above say 300kHz and below say 0.01%, do better numbers equal better sound?  My indirect experience says after achieving these specs, focus on other elements of the circuit or internal components to optimize the sound by ear and less-conventional numerics.

Also, for many of these specifications, there isn’t any internationally agreed-upon measurement technique or standardization for something like peak current. An amp may deliver 60A peak for a millisecond, but any musical transient is much longer than that. But for 250 ms, that same amp may only be able to provide say 20A, and perhaps 8A continuous.
The last time I believe this was standardized was the IHF dynamic headroom measurement, which was how much more power was available on a 20ms toneburst than on a continuous basis. But even this method was compromised as it was found that most fast musical transients are in the 80-200ms range, and I don’t believe a 200ms dynamic headroom test was ever standardized. Others may correct me.
Back when this was part of an amp’s specs, a doubling (spec'd as 3dB) of the continuous power output with a 20ms toneburst was considered respectable.

sdecker- when Jim developed the equalizer, that transient burst factor became obviously clear. He determined that an amp needed to deliver triple its continuous output for about 250ms to properly cope with a broad variety of music. He used that assumption when boosting the bass with EQ to take advantage of power that would, on average, be available in the bass. That assumption proved to be problematic in that many amplifiers, especially spec-driven designs, fell apart when asked to deliver transients while delivering augmented loads to the equalized bass. Some amps do a wonderful job in the series 1 and 3 equalized bass. But others don't, and sound bad, and burn out tweeters.

tomthiel -- and I presume his determination applied to the amplifier's ability to triple its short-term output into the lowest frequencies, the most problematic for any amp.  I believe the IHF dynamic headroom test specified 1kHz, which obviously had little-to-no bearing on the amp's headroom into the bottom octaves. 
Manufacturers were then spec'ing continuous power output over the full 20-20k Hz bandwidth, but many of those amps were tapped out at 20Hz.  Ask them for more power at those frequencies and it's no surprise they'd clip and burn tweeters,
How many amps of that era actually had the balls to triple their continuous output for 1/4 second at 20Hz into a demanding Thiel load??  That sounds like quite a feat for even today's best amps!

Our early amps included Phase Linear 400 and Threshold S500, which turned out to be non-representative, leading to an error of judgement.
I think the way Jim looked at it was that the tripling at 1kHz allowed for midrange transients beyond rated continuous power and that those peaks rarely coincide with bass transients, therefore the working headroom.

Error, or hindsight, or fudged specs, the EQ gave Thiel some notoriety in the amp department. I don't think Jim ever got the amp demand part right (from a market viewpoint). If his design loads maintained 4 ohms minimum, the speakers would be so much easier to drive and the voltage sensitivity and current demands would be in sweeter equilibrium. That's my layman's opinion from the user peanut gallery.