Lyon and it's not even close. And I rate Harmer pretty highly.
My read has always been that, even though they're similar in having bounce as a main weapon, Harmer's is generated more from his height and his action height whereas Lyon's is generated more by overspin. That means Harmer can turn the ball more in terms of sidespin, but is lacking in the flight department. Meanwhile Lyon isn't as big a turned of the ball, but has a greater ability to use flight.
The extreme majority of the time at the elite level, you'll need to beat the batsman in the air, not with turn. If memory serves, there was some analysis from PEWS years ago along the lines of this point explaining why Lyon gets better the higher the level he plays.
On top of that, Harmer has a tendency to drop a little short and bowl a little straight. That often negates the benefits of gaining extra bounce, letting batsmen hang on the back foot and work to leg. It's exactly what happened at Taunton last season - Hildreth looked the most comfortable batsman and was predominantly playing back and leg-side, while all the other batsmen who insisted on pressing forward kept getting into trouble. But the plumb in front while playing back dismissal that gets Hildreth looks so much worse in a highlights package that a procession of batsmen 'getting a good one' that they nick to slip (but I digress).
Absolute credit to Harmer though, he knows his game extremely well and has both the skills and the cricketing IQ to absolutely tear through county teams and do well at the domestic level. He's a serious off-spin bowler. But I can't think of many (if any) situations at Test level where I'd rather have his style of off-spin bowling over Lyon's.