Disclaimer: These are my findings based on the DC version. I’ve just read that the damage of s.hp within Genei Jin is generally more than the Palm - as opposed to the arcade. How accurate these are I don’t know. I highly doubt they are but of course I could be wrong.
I suppose it looks cooler but i don’t think it’s more damaging than using s.hp instead of the palm and ending with the regular finisher. (ie chain, activate, s.mp, f.hp, f.mk, f.mk, s.hp, f.mk, f.mk, s.hp, (another s.hp for some chars), shoulder, shoulder, f.hp, lunge punch.
afaik, the only time to use the palm (in the corner, and other than for cosmetic purposes) is somewhere near the start of the combo - say after s.mk, you can do palm then kara palm. otherwise, if you start with the chain combo, u should only use the palm if you added the shoulder (to gain that extra bit of meter) to the chain before activating geneijin. even then, for max damage, it’s best to use the regular finisher instead of the more popular (palm, dp with k, lp shoulder, f+hp, lunge punch) as it (the regular finisher) is much more damaging (admitedly, variety do make the combos cooler to watch).
sorry for not knowing the names of specials.