From my experience, I find NGC to have looser grading, that is, a coin with more contacts marks and scratches can attain a higher grade than the same in PCGS. However, PCGS are less consistent in their grading, albeit prophesying to uphold higher grading standards. NGC are more consistent within their more liberal grading.
When it comes to auctions I'm not sure. If I get a coin graded MS63 in PCGS it will value at X price approximately. If however, the same coin I send to NGC it might grade MS64, however, since the grading is known to be a little looser, it will garner a lower price than a PCGS MS64. This scenario has actually happened on three coins I'm aware of.
What I just wrote was a very simplistic form of appreciating the difference and I'll stand corrected my many :-) I tend to agree that NGC are more technically inclined whereas, PCGS more market grade driven. The big concern in my opinion is the consistency. This causes for a lot of heartache to collectors, because that difference of one point does impact the value of the coin, should it not be appreciated by the bidders.