There aren't so many surfaces but it's pretty clear Djokovic is a better HC and Clay player.
Federer is a better Grass player.
Grand Slam Titles
Hard: Djokovic 13 > Federer 11
Clay: Djokovic 2 > Federer 1
Grass: Federer 8 > Djokovic 7
Winning %
Hard: Djokovic 84,8% > Federer 83,3%
Clay: Djokovic 80,4% > Federer 76,1%
Grass: Federer 86,9% > Djokovic 85,8%
GS Winning %
Hard: Djokovic 89,0% > Federer 86,8%
Clay: Djokovic 84,2% > Federer 81,1%
Grass: Djokovic 89,6% > Federer 88,2%
Let's talk about peak level
Best GS Tournament
Hard: Djokovic 2011 AO > Federer 2007 AO (None of them had his best HC tournament at USO)
Clay: Djokovic 2013 RG > Federer 2007(?) RG (Federer never battled prime Rafa like Nole)
Grass: Federer 2005 WIM > Djokovic 2015 WIM (Anderson's match make the difference here)
Best Season
Hard: Djokovic 2015 > Federer 2006 (Very close but, with tie at 2 GS, WTF and 4 M1000, Djokovic had 2 M1000 F against an early exit in Cinci by Federer)
Clay: Djokovic 2011 > Federer 2006/07 (What season you choose depends from how much you value M1000 against RG, but it's not close here)
Grass: Federer 2005 > Djokovic 2015 (Not much more than Wimbledon in grass season)
Best opponent beaten(GS)
Hard: Djokovic def. Federer at 2008 AO > Federer def. Agassi at 2004 AO (Djokovic had several wins against prime Fedal, I'm not sure which was the best opponent beaten by Fed in HC slams, a #7 post-prime Agassi? a pre-prime Nole and not 2010 one? A 2014 Murray, prime but in a bad season?)
Clay: Federer def. Djokovic at 2011 RG > Djokovic def. Nadal at 2021 RG (Arguably, a win over Nadal is always more impressive at RG)
Grass: Federer def. Djokovic at 2012 WIM > Djokovic def. Nadal at 2011 WIM
That's not much, but you don't need to go deep when results are pretty clear by a basic analysis.
It would be interesting talking about indoor(Or indoor HC) as a surface, I think that would be pretty debatable.