The 530d is quite obviously the superior car to the 520d.
It is faster, smoother, more refined and has a better standard specification - the 520d has only the basic climate control, the 530d comes as standard with the Climate Control with 'Extended Features' (Which are things you'd expect as standard, like a sun load sensor and more adjustable of ventilation speeds).
The difference in fuel efficient isn't major - in my experience (My Dad runs 520d's, I've had two 530d's) the fuel efficiency difference is circa 10%. From mid 2015 the 520d got an all-new engine - I've no useful experience of the efficiency of that engine but it's unlikely any of those will be in budget.
However the downside is that the 530d's are both much rarer and considerably more expensive than the 520d. There are numerous 520d and it's really not difficult to find a good LCI 520d M Sport with M Sport Plus and Pro Nav quite quickly. The same cannot be said for the 530d - mine took half a year to find. There is also a large price difference - £20k easily buys a nice LCI 520d but you'll struggle for a 530d. The equivalent 530d can often be between £3k and £5k more expensive (The gap was even bigger new).
Essential options are Professional Navigation (Professional Media Package is the same thing - all M Sport's with Pro Nav have Pro Media Package which also includes BMW Connected Drive services) and automatic gearbox. The rest are nice things to have rather than essential, the LCI already has Xenon headlights etc as standard equipment and leather has always been standard on an F10.
LED headlights, forget it, you'll never find a 520d with those fitted. Things like MFD again nice to have but really not worth hunting out or paying extra for. Audi Virtual Cockpit it is not - it does nothing the Full Black panel display doesn't also do, it's just the same information presented in a different and more digital way. The Audi system is considerably better and well worth having.
LCI cars built after March 2014 have Full Black Panel and Tyre Pressure Monitoring as standard.