I know the CC and Playoffs are supposed to be neutral site games and they don't appear as Home or Away games when you view your record for the season (It's always just the 13 regular season games).

 

However, I seem to notice that my team plays better when they are listed as the home team and plays worse when they are listed as the away team. Has anyone else noticed this with regard to their teams? Has anyone done any research on it?

I've never done any true research on it, but my guess is that you're seeing too small of a sample, and any pattern you see in your neutral site games is coincidental.  It's still a pretty small sample, but just glossing over some of the postseason games I see in one of my worlds shows no correlation.

Also note, that if you do look at the postseason for non-D1A, you have to remember that the higher seeds are generally listed as the home team, and therefore, it would make sense if they won a little bit more often.

Yeah you could definitely be right ... it's also probably because I only notice that when I lose games I feel like I should win ... just trying to find some way to justify it instead of attributing it to the randomness of the engine.

I've never paid attention.  I've never noticed any kind of home field advantage even in the regular season either.