Unsure if I catch your drift on this one.
'If that is true, then Federer picked up more slams than Nadal did, even if you count WAY after Fed's prime, since Nadal began winning slams.'
Federer's prime - 2004-2007? Nadal RG champion 2005.
'picked up more slams than Nadal did?'
2008 - Fed 1 Nad 2
2009 - Fed 2 Nad 1 (Nad absent Wim)
2010 - Fed 1 Nad 3 (Nad retired AO)
2011 - Nad 1
2012 - Fed 1 Nad 1 (Nad absent USO)
or comparing Federer '03-'07? to Nadal '05-'09?
Federer wasn't dealing with Murray & Djokovic in '05, '06 and the first 3 majors of 2007, wasn't suffering injuries at majors and major absences.
'Fed's prime' - 2009 GS results = RU, W, W, RU. Wimbledon champion 2012 - his play wasn't as great as in 2006 but Fed's prime is up to interpretation.