The 3 players who stick out to me are Griner, Holdsclaw and Parker. Griner sticks out because there is a very good possibilty UCONN literally goes 4 straight years with undefeated seasons during her time there. You'd have 2 years of Moore/Griner, and Griner as an upperclassmen with the core group of players who won the 2013 title and Tiffany Hayes makes them the obvious title threat in 2012 and 2013.
With Holdsclaw and Parker, UCONN didn't win a title while either of those players were at UT. If Parker is on UCONN in 2006 they probably don't win the title (although, it wouldn't be a big surprise if they did) and they'd be the obvious title threat in 2007 and 2008 with Candace Parker as a sophomore/junior. If Parker plays in 2005, I don't think UCONN wins a title but would be a strong Final Four threat and having the presence of a go to player like Parker might enable UCONN to find its identity and make a championship push. I'd guess UCONN wins 2-3 more titles with Parker in the lineup.
Put Holdsclaw on UCONN in 1996 and they are overwhelming title favorites, same thing again in 1997. 1998 you'd have Mique/Sales/Abrosimova, and in 1999 Ralph/Holdsclaw/Abrosimova and TASSK. Very realistic that with Holdsclaw, UCONN has 4 more championship banners hanging and Tennessee has 3 less.
As a UT fan, outside of Taurasi as being a player who I think would've enabled Tennessee to win more championships (at least 2, maybe 3), I would choose Seimone Augustus. Augustus would've given UT the offensive scoring punch needed to get over the hump in at least 3, maybe all 4 of those years in my opinion.