I have both a Tikit and a Brompton. Having ridden both, here are some thoughts.
1. Even though the Tikit can be rolled around while folded, you need forearms the size of Popeye's to roll it any significant distance. The weight distribution of the Tikit when folded forces the bike to lean to one side, forcing the rider to twist to keep it level to roll. The Brompton, with OEM rollers, sucks to roll while folded even more. I put roller blade wheels instead of the EZ Wheels on the Brompton and I prefer to roll the Brompton than the Tikit. My girlfriend rolls her Brompton everywhere and she weighs 112 lbs. It really is effortless on the Brompton. Also, on the Tikit, the chainring is still precariously close to your pant leg while rolling, unless you roll it from the right, keeping the chainring guard between your pant leg and the chain.
2. People keep dismissing the size difference between the two as insignificant. I consider the size difference incredible for my uses. I can fit only one Tikit into the trunk of my VW Golf. I can fit my TWO bromptons and still have room for at least one more in the same trunk. I could probably stick a fourth one in there, but I have not tried it. People keep spitting off dimensions of the Tikit while folded, without the front rack!
3. The Tikit's chainring is very close to the ground while folded. I've had a couple incidences where the bike tipped over or became lopsided, and I had to clean the chain grease off white carpet. I've never had that issue with the Brompton. Even though people would not put a bike on lighter color carpet, it's something to consider.
4. The Tikit, at least the older ones (one of which, I have), needs adjustments out the wazoo to keep it locked while folded and to keep it stable while folded. I have an older style Tikit, and constantly have to keep bending the locking latch that clicks to lock the bike while folded. If it becomes too relaxed, it won't stay folded if I lift the bike. Newer style Tikits have a different latch mechanism, but I doubt it's dramatically better. It's still a latch that slides over a peg and locks. It's still a piece of metal that bends to lock. My dad has the newer style, so I guess I can try it out next time I visit him. I have the rear rack too, and while it helps stabilize the bike while folded, if the ground is anything but level, it's a pain to keep it upright. The Brompton is very stable while folded, but since I put roller wheels, I need to place it in such a way that it doesn't roll away
I modified the Tikit by replacing almost every component with standard bike parts from online retailers and local bike shops. I can't do that with the Brompton, which is a pain in my butt, since I want to modify the gearing.
Both are great bikes. I've ridden the Tikit on a metric century and my girlfriend rode her Brompton. After that experience, I can tell you that I'll never ride a Tikit or a Brompton on a metric again!
Out of the two, I like riding the Tikit for longer faster rides and the Brompton for shorter more casual rides.