It's such a broad question and there are quite a few angles to tackle it from. When we talk popularity are we talking amongst the truly hardcore cycling fans, or do we include the July fans as well?
Alberto Contador is the most popular active cyclist in the world. He's also the most popular current cyclist on this forum, though it would be interesting to see a poll that ranked him against past greats, as this is a forum of (mostly) informed cycling fans.
Obviously here on this particular site Armstrong will be a ridiculed choice, but he does have a lot going for him. Hitch pointed to an advanced marketing campaign to bolster his numbers. And there is truth in that. There's also truth that said marketing campaign worked. Armstrong is famous, make no mistake about it, in America and the World. There is the other argument that cycling in America is not nearly as popular as it is in other countries. True, but also a touch flawed. America's population is greater than Italy/France/Germany/Uk/Spain/Belgium/etc/etc/etc combined. And Lance clearly drove numbers in America. He was a Giant in the country. Practically everyone in a country of over 300 million people knew his name. There was a time during his run where you'd have a hard time finding anyone in the country that had a negative opinion of him. He was charitable and marketable and dating a rockstar and hanging out with presidents and his face was on every billboard and commercial and gatorade bottle and wheaties box. Kid was famous, and well liked, and well respected. I'm spent most of my life here in the states so I can't speak to his popularity in France/Germany/Italy and elsewhere. I'm not sure how popular he was in those countries. I can't imagine however that he had no fans at all. Anecdotal musings about how true cycling fans always hated him aside he did have sponsorships in countries other than the USA. The last dismissal of Armstrong was in saying that his twitter and facebook numbers don't matter. He has 4 times the number of twitter followers that Contador has. His facebook numbers are equally crazy. For a man who's popularity peaked before the advent of modern day social media that is impressive. Is he infamous more than famous, or anti-popular more than popular? probably/possibly, but those are the numbers we have and they suggest an athlete that transcended the sport in ways Contador never has. But I digress, I actually went farther afield than I meant to.
What I meant to say is it's difficult to have this discussion during a current cyclist's reign as it were. Contador is at the height of his popularity. He is highly respected (and I think beloved) amongst the core cycling community. He just won his 9th GT and he did it with class. But... He is not as popular now as Armstrong was at his height of his fame. At least not with the people who watch cycling in passing, or even the ancillary cycling fans who'll watch the Tour and maybe one or two local races. With the hardcore cycling fans, yes, he's probably as popular maybe more so. It's tough to quantify and I don't know that there's any wrong answer.
Unless you say Froome, Froome is the wrong answer.