Why DIFFERENT op-AMP in parallel (AD826 and LT1364) can sound better ?

Paralleling opamps without output load-sharing resistors is a bad idea -- the opamps may "fight" each other.

even with load sharing R it still doesn't work for multiple op amps to share the same feedback - op amps have huge open loop gain and vary in gain and input V offset by too much for them work by literally paralleling  the pins

each op amp must have its own feedback to control the open loop gain

only buffer amps with internal unity gain feedback can sometimes be paralleled

I would expect that if you looked a the op amps output pins you would see only one actually moving with the signal and the other(s) saturated - stuck near either the positive or negative supply V

the link in your 1st post shows the "wrong" way

fig 1 in the intersil link is known here as the "A47" cirucit from the Headwize article and works, fig 2 in that app note has problems

I have showed that you can Class A bias op amp outputs with a variation of the paralllel "master/slave", output current copying scheme

http://www.head-fi.org/forum/thread/188758/ad8397-class-a/15#post_2264079

the 47 Ohm current sense/share resistor values can be less - which gives better stability with cable capacitance loading the output

I also point out a way around the op amp common mode input limits of many op amps using the "A47" scheme in my posts in the above linked thread

I build composit circuits related to Jung's Multiloop - one op amp is chosen for input characterisics and controls the outer feedback loop around a higher output current, faster op amp which drives the 'phones

you could unbalance the load sharing resistors in the "A47" scheme to get more current from the "slave" op amp and use one with better input for the "master"

for Class A push-pull output bias in my posts the two op amp's output current capability should be better matched - each op amp supplies the full current at the peak of one half cycle

you don't have to have bias Class A for the full range - say for only the 10-20% of the range near 0, then both op amp's output currents add near the peaks - this would be a "heavy" Class AB bias in accordance with Nelson Pass' First Watt site's opening comment:

"Dick Olsher famously remarked that “The first watt is the most important watt."

if you don't want the Class A push-pull, rather than using the parallel scheme I'd just pick a output op amp with enough current drive on its own - like the TPA6120, LT1210 or AD8397