I have a Cateye Double Wireless, and I was surprised at how much the tire circumference in the instructions varied from what I was measuring and observing.
I run 700x25C Gatorskins, and the Cateye instructions said to use a circumference of 2105mm, but I was measuring a circumference of 2155mm, when the tire was inflated on my wheel. That's more than a 2% difference. In actuality, it can be shown that the Cateye number (2105mm) is a lot closer to the true circumference (when a rider is on the bike, compressing the tire, and changing the effective radius of the wheel/tire and circumference of the tire) than 2155mm is. So if you can live with a small amount of inaccuracy, I would say that you should go with the number in the instructions that came with your computer. It's probably something they've considered more carefully than you might think.
I tried to explain this to a friend, and his reply was "your inner nerd is showing," which is probably true. But, I have degrees in math, and I don't care.
What I found, for my bike & my weight, was:
1) Sitting on the bike causes the tire to compress about 5mm. (My computer sensor reads off my back wheel, which carries most of my weight.) So when I measure the circumference of the tire, that must be taken into account. There is, effectively, a loaded and unloaded circumference. In my case, the unloaded circumference of a new 700x25C Gatorskin is about 2155mm. The loaded circumference is around 2124mm.
2) The tire wears over time. With 3200 miles on the rear tire, it's squared off pretty good, and the worn unloaded circumference is about 2140mm, whereas the worn loaded circumference is around 2109mm. These tires are typically good for 4000 miles, maybe 4500. Near the end of its life, the number given by Cateye turns out to be pretty close for this tire. But not all tires of a given size have the same circumference. Schwalbe Marathon Plus tires, for example, are taller (larger circumference) than Gatorskins.
3) Can I find a "set it and forget it" number? I could just use the figure supplied by Cateye, 2105mm, or I could interpolate and use (2124+2105)/2=2115 (rounded). Over the life of the tire, this would cause my speed and mileage to be overestimated when the tire is new and underestimated when the tire is worn, but it should average out by the time the tire is replaced, assuming the tire achieves an average lifespan.
2% is not a huge error, but over a year's mileage for me, it would cheat me out of a longish ride's mileage (somewhere between 40 and 50 miles), at least in my records.