John
I am of the impression that there is a sonic difference but am very unsure of that notion. 
 
If there was any processing in either DAW that may account for it. This could be as basic as what pan law was used. 

No processing whatsoever, both instances of Native Instrument's Battery  in both DAW's were routed out to the sound card main outputs, bypassing even the bussmaster.
 
Pan laws were the same (0 sides, -3db center) + it was a stereo instance of Battery loaded on a stereo track.
 
 
Yep, there is a subbtle sonic difference!