Bicycle Tutor

Today more bikes use Aheadset instead of the Quill stem. I would guess the Aheadset is better or they wouldn't be using it but I would like to understand why. What are the advantages and disadvantages of one style of headset over the other?

I assume you mean a threadless stem versus and "quill" stem for a threaded fork.
The main advantage of threadless for the rider is lower weight. The main advantage for the manufacturers is lower cost.
Disadvantages of the threadless style are that you generally have less ability to adjust the height of your bars since you can't just slide the stem in and out of the fork. However, you can make some adjustments by moving spacers around or flipping the stem over. Also, you have to be very careful to avoid getting corrosion on the steerer tube of the fork. It can make adjusting stem/headset a nightmare.
Threadless set ups require a fork, stem, and headset that are all designed for threadless. Likewise on threaded. Though there are some adapters out there that let you use a threadless stem on a threaded fork/headset.

You are correct in assuming I meant threaded vs threadless. Thanks for your input. The last time I rode a bike was in the sixties. I got my license and first car in 1969 and haven't ridden since, until last summer. Now I'm hooked and trying to educate myself. Thanks to folks like you and sites like this I am learning. Thank you Dave and all of you others out there too.