I think he's improved, here's why....
Being older, he knows people are less 'afraid' to challenge and hence as a result has worked harder because of it since he's still hungry to win.
Back in his prime, Federer was cocky about his backhand. He knew players target it day in and day out and the errors would eventually come from that wing, but back in the day he could shrug it off because he always found a way to win (most times).
Now, IMO, he's hitting his backhand with far more confidence than he did during 2008-2010. He knew he had to improve it, and it shows.
Additionally, Annacone has stressed the importance of a strong serve. Hitting your spots, having variation with spins/speeds and the importance of a strong second serve is (in my honest opinion) the fundamental reason why Federer's been able to have a significant presence in all the slams.
Federer's serve started to drop off late-2009/early 2010, the second serve was a huge liability with poor placement, even his first serve didn't particularly hit the spots and his toss was quite lapse. If you watch any videos from 2008/09 and compare the motion of his serve to now - it is more consistent.
Federer's able to race through service games in 60 seconds is probably a reason why he's been so injury free for so long lately, he's not struggling to hold service games and hence not punishing his legs by slugging out service games in the process in the process a la Rafael Nadal.
Q: How close are you and Djokovic?
Murray: Well he's in Dubai and I'm Doha, so around 450kms