The Porta Corda uses very high speed high performance op-amps. The crossfeed is substantially different from headrooms, and takes more getting used to (for example it does the opposite of bass boosting). A lower setting may have been a better default, but I think I'm getting used to Jan's crossfeed. It removes stereo seperation to a greater extent than headrooms IMO which is good or bad. Definitely takes time to get used to if you are a headphone nut. Although Jan's crossfeed is supposed to be the "natural" one, it is headroom's crossfeed that I would say is the more subtle one. However I can definitely say the highs remain clear and detailed with the PC (just without the extreme seperation).
Also the PC comes with a very good mini-mini cable as well as the 120 ohm adapter which is useful if you have those Beyers.
I've had a few CHA47 type amps, and the PC is a higher performing amp. However, I would be hardpressed to really say if it really is that much of an advantage in portable usage. The Bur-brown opamps used in the typical CHA47 design is a favorite and while probably beating the crap out of the typical default headphone jack, still remains a bit more forgiving than the opamps used in the Porta Corda. IMO the Porta Corda is a faster amp with tighter bass and clearer more detailed highs, however these elements can be harder to appreciate in a portable setting compared to the rounder bass of the OPA132/134. The OPA132/134 does the job, and has just the right touch of warmth to be forgiving for portables.
I've had the older TA and will hopefully try a new TA sometime in the future. The Headroom portable amps are usually always leaders in terms of battery conservation compared to the other alternatives. The *older* TA I had lagged a little compared to the alternatives only because I really didn't like the DC-DC convertor. The new Headroom designs take out the DC-DC convertor which should give it even better battery life and I really can't wait to hear the improved sound and best of all cleaner background with no hiss! (at the expense of using less conventional battery types, but AAA's nimh's are still easily obtained). Battery life is important and understated in comparisons often...it is sometimes unfair to compare two fresh battery amps in sound quality, when in usage it can be the more efficient amp that wins the day in real portable applications. I had a 2 9V CHA47 altoid tin before, and it was just a pain in the ass when it came to batteries even though it was a great performer sonically.
There really is NO consensus or general opinion about the ranking of these amps. The *older* TA and airhead may have lagged slightly, but it is basically preferences and different compromises now. If you want a recent AB comparison you should read Ross's findings with his Ety's. Maybe I can chime in later when I get my hands on a the 4.5v TA (although it is the 9V TA which would be a more fair comparison, I'd rather get the battery life).
Since you have ER-6's I'd say to save money for ER4X series headphones for improvement in the portable arena.