I have both and use both, though I've used Navigon more than TomTom. I bought Navigon soon after it was released, but found it lacking enough to buy TomTom the day it was released- which I found it also to be lacking. Right now, both are pretty strong, and I'd hesitate to recommend one over the other. But I can offer my thoughts on the two.
Navigon wins the popularity contest. They are clearly out to win the iPhone GPS turn-by-turn market in the US. They don't even sell GPS units in the US, and their US subsidiary has put all it's chips on the iPhone app for it's survival. I believe this is why, in general, they arrive sooner to market than TomTom with "flashy" features that users are most vocal about- text to speech and live traffic, but no route list view, and no straightforward way to avoid certain roads (TomTom had these from day one). TomTom is slowly but surely following suit in matching Navigon feature-wise, but they may never overtake Navigon in sales. But I wouldn't be surprised if they end up offering a better product over the long haul. Take IQ Routes, for example- TomTom just ported it from their standalone GPS software. Navigon has nothing like this in the US and would have to bear the full cost of developing it from scratch. Meanwhile, it seems to me that right now, Navigon's rerouting based on live traffic is useless- or worse, to be intentionally avoided (it cost me about 15 minutes yesterday due to poor traffic rerouting). I'm not saying TomTom will probably eventually overcome Navigon in the long run based on functionality, but it's possible.
One significant difference between the two that will likely remain over time is the user interface. Navigon is slicker and looks prettier, by far. It's enjoyable to use and to look at. TomTom doesn't look like much, but is much more functional and utilitarian. Navigon wins hands down when you are using it on your hand. Mounted on a windshield, TomTom is easier to follow and read- even street names are easy to read when you're driving (not so with Navigon).
Which is best, or which should you buy? I don't know. Both are strong, and both will get better and better- and probably closer and closer to each other in terms of features- over time. Navigon is the little engine that could (at least in the US market), and they are intent on being the dominant player in the iPhone market. TomTom is the slower, more plain, but more functional "big company" alternative with lots of leverage in the business and a more professional approach (can you say "feature documentation", Navigon? Didn't think so.). [Can you say "we really are trying for the win the race" TomTom? Didn't think so.]. But really, I don't think either will ever be a major disappointment compared to the other moving forward.