I wrestled with this very question 2 years ago. Did a lot of research (there are great demos of how both bikes fold on YouTube), and the consensus was…

Brompton: best folding, smallest package, pretty good bike
Tikit: fastest folding (but into an odd shape not quite as handy as folded Brompton), better than Brompton as a bike

Since I wanted to bike commute and then "smuggle" my folded bike into an office building every day, I went with a 6-sp Brompton. I like the way it quickly folds into a neat little squarish shape and how, with its cover on, it never draws the attention of office building guards, and I really like how it rides, too. It's so cleverly thought out, and has a kind of smart, British elegance about it. As I said, most people feel the Tikit is a better bike, and I nearly bought one. But the Brompton's tidy folded package – plus the fact that it's been made and refined for over 20 years now - persuaded me to choose the Brompton.

For bopping around Manhattan and the rest of NYC (which isn't particularly hilly), the 6-sp Brompton is perfect. The occasional longer ride? I wouldn't hesitate to take the Brompton out on up to a 40 or 50 mile ride over gently rolling terrain. But for rides longer than that – or more serious hills – I believe any Bike Friday would be more suitable.