This thread is likely to spark some debate...

Overall, I'd rate BA over EK. However, purely for LHR, I'd probably recommend EK due to the superior and consistent A380 product - not like the B777 or A330/A340 fleets.

In no particular order:

Schedule: EK, with 6 flights daily to LHR and 2/3 to LGW, more choice than BA's 2/3 to LHR
LHR lounge: EK (vs. T5 Galleries), plus convenience of boarding from the lounge
DXB lounge: EK's A gate lounge (most A380 services) beats BA's poor terraces offering, EK's B gate lounge (some A380 services) is also poor but with better food and drink
Inflight hard product: EK A380 all the way
Inflight soft product: Not much in it
Pre- / post-flight: EK, chauffeur service is very useful.

That said, Skywards isn't a great programme. You'd be gold after five returns on EK and would have 50k miles (as a benchmark, a return in business is 90k). However, their upgradeable fare buckets are restrictive. Also, where are you based? Do you want to fly through DXB for your holidays?

On BA, you wouldn't (quite) be gold, but would have the same c.50k miles (as a benchmark, a return in club is 80k), but these are arguably more valuable for MFU / UUA.

Reward availability on EK does seem to be a lot better than BA - although still isn't perfect.

However, for me, I nearly always take BA as EK have a consistent habit of dropping the ball on most other routes, leading me to somewhat dislike them.