It's the sound of Gretsch that attract me. I play (ed) in small jazz groups for years and a lot of the jazz guys played Gretsch. I didn't get it, either, until I played a small bop sized kit that a friend of mine had gotten. As soon as I hit the tom, I knew there was something different about the sound....noticeably different. It was that sound I had been hearing on the recordings I was listening to at the time.
I think some of the sound of Gretsch actually may have had to do with the fact that the Jasper shells were often oversized and didn't have the greatest edges on them...So the jazz guys had to tension them waaaay up to get them to sing. That's a theory, anyway. Also, the shells didn't have reinforcement hoops...but the die cast rims made up for that stiffness...maybe something about the greater mass at the ends of the shells allowed more of the shell to resonate -another theory. Bottom line: They were made differently than the other Big Four companies and they sounded different....Any qualitative comment after that is always going to be based on what sounds good to your own ear.
Ironically, I've never owned a Gretsch drum in my life! -played a few in the studio...loved them! I'd love to get a nice RB bop kit, though!