John,
There are a plethora of differences between the two. Cost being the most notable. As you have certainly noticed, a hand held unit cost much less to buy, but is also not as convenient.
The cost and installation of a hard wired unit is considerable, but so is the convenience. Being able to keep track of the the wind direction and speed, especially when using the auto pilot is, as the credit card says....Priceless.
I don't race, and when we are out I love setting my sails to a wind that is some where between 60 and 90 degree off the bow. The auto pilot is set and we relax. A quick glance at he wind indicator periodically tells me I need to adjust my AP either up or down a couple of degrees, which is much easier than adjusting sails. You can as you check the wind direction also check the wind speed
If however you want to only know the speed of the wind, a hand held is great, and the price is so much less and when it breaks and they all eventually break the cost is so much less.
If you are on a budget and only want to know the wind speed, go hand held.