I've actually been toying with the idea of using aspects in D&D.

Most modifiers give a +2/-2. 

Myself and other people who've DM'd have used various Role playing points/Luck Points etc.. to let players save up to buy extra feats or buy skill points.

I think adding the aspect system would enrich the game.

An interesting facet of 5th edition D&D is inspiration.  Characters have two personality traits, one ideal, one bond, and one flaw.  If you play out your personality traits, the DM award you with an inspiration point.  This can be spent to roll and extra D20 on a roll and then take the highest.  It has a low level fate point/aspects vibe.  They even give advice that sounds like it came straight from FATE.  An example is not to use the trait "I am smart" but rather "I've read every book in Candlekeep" becuase the latter says more about you.

I am getting ready to run a 5th edition campaign and am considering adding a more robust system that includes Declarations and such.