How you punch and kick in tae kwon do, or any karate style for that matter, may be very different from how you punch and kick in eagle claw. You may use your body and hip to generate power differently. So a good way to kick for tae kwon do may be no good for your eagle claw. Also you may be able to duplicate the motions because you have previous training, but you may not have the right energy behind it.
I had some experience in tae kwon do and karate, and it is quite different from how i punch and kick in kung fu. Now I am so used to kicking and punching the way my kung fu teacher has taught me it feels weird doing it the tae kwon do or karate way.( Every once and awhile I go to a karate class to do a little comparison).
A good hard punch or kick will still hurt somebody no matter how you do it, but different styles will have different preferences on how they do things. You may also find trying to do eagle claw and tae kwon do at the same time may slow down yourprogress in both, since they may be more contradictory than complimentary.