Although I am sure there are others on this board that have vastly more experience with what you are asking, I have done this many times. PSA certainly permits you to submit "crossovers" for grading. In my experience, I have never received a higher grade from PSA than the card was graded by SGC, and often the PSA grade was 0.5 or 1.0 grades lower. Thus, one needs to be careful crossing over high dollar value cards, as the subsequent "value" of the card may be hurt by a lower actual PSA grade (I am specifically not jumping into the maelstrom of the pros and cons of each of the third party graders and why it may benefit PSA or SGC to perceived as more stringent with grading). Therefore, for instance, if you were assembling a PSA 5 set and you were trying to cross over a SGC 60 to PSA, you might be disappointed with the result (although you can always submit the card with a minimum acceptable grade expectation, running the risk of getting the card back as not crossing over given your stipulation). Sometimes, it may be worthwhile cracking the card out of the holder before submitting to PSA, as (I feel) you may get a more objective grading of the card.
Out of full disclosure, I have never submitted a PSA graded to SGC for crossover, so I have no experience in the reverse of your question. Also, although I completely understand your trepidation regarding cracking out a card from its holder, SGC (and for that matter PSA) holders are actually quite easy to open, if done slowly and carefully (although practice on a low value card first just to understand what is involved).
Just my opinions and have a Happy Holiday!
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