I've had pretty thorough experience with NT01s, since this I'm on my 3rd set at this point. Couple of things worth mentioning:
1. NT01s are an R compound tire, designed for competition use. This means that they have a certain purposed in life, and that’s not street driving or street performance. NT01s are highly sensitive to temperatures, which means that if you are outside of the working temp range (around 200 degrees or so), they will not provide optimum grip. What that means to an average user is that they will not yield any more grip than a really good high performance street tire, if they are cold.
2. The tread design is basically made for two conditions: Racing in wet, and racing in dry. In off the shelf form, the tire has 6/32[SUP]nd[/SUP] tread depth, which is actually really good for rain events, if you can keep the temps in the tires. When shaved down to 3/32, the tire becomes a fully slick surface, except two grooves in the middle of the tire. This is for optimal dry weather utilization.
3. R compound tires have a limited quantity of heat cycles before the tire does not work as well as it used to. Street tires are less sensitive to something like this, so it takes a while for them to stop working as well as they used to. Usually you will be down to wear bars at that point. NT01s will get there a lot faster. I use mine only at the track, and driving to and from the event. When not in use, the car is stored in dark garage under the cover. Simple cruising around for no purpose is out of the question.
Personal notes: If you are looking for street tire with capability of autoX, NT01 is not for you most likely. There are tons of street tires which will grip just as good as NT01, and will last longer, as well as get up to temperature faster. Check out NT05 from the same company, they are very popular with auto enthusiasts. The main difference between NT05 and NT01 is how durable it is at the limit over an extended period of time. NT05 and NT01 will probably post same lap times on the same car for the first few laps, after which NT05 will start falling off, while NT01 will remain consistent. I can do a full 30 minute session on NT01s, and the street tires will usually give up after about 10 minutes.