I only use the button on the embroidery machine...
On regular piecing or quilting I prefer the foot controller. My machine also has a red square next to the foot controller so that you can touch it and cut your thread. I had to disconnect it from my machine...as I have a cute little dog named Tinkerbelle who likes to plant her fat little butt right on the red button.
She kept cutting the threads on me all thru a seam...until I figured it out....figured the machine was going crazy!

start/stop or foot pedal
 

I use my start/stop button because I got ankle tendonitis from too much sewing and am still dealing with foot problems from over use.

I am still deciding if there is an advantage over one over the other method. Health is certainly one consideration if one is in the market.

At this point, I have the foot pedal attached; no knee lifter or start stop in use.

As always, very interesting. When I was a child my grandmother got me started on her treadle...them my Mom's machine had the knee lift. My machine doesn't have a start/stop, just the foot pedal... Don't think I could do it...maybe I'm too old to learn!!

Depends on what I am doing but most of the time I use the foot pedal.

All it is is an option on some newer machines...if your foot pedal is plugged in, your machine will run from the pedal in the way we are all used to. If you unplug your foot pedal and your machine has the start/stop button, then you use the button in conjuction with a slide switch...the slide controls your speed...so you put it where you're most comfortable..then you push the start.stop button to sew or stop sewing. It is usually located where it is very handy, so you barely need to move your hand to reach it...here is a pic of a model with this function...they are on most machines now from 120 dollar cheapies all the way up to high end makes...
https://encrypted-tbn0.gstatic.com/i...I-OAU5awQGxtMw

here is a better pic..
https://encrypted-tbn3.gstatic.com/i...V5cWTbbITDFHywand here is the speed control slide...
https://encrypted-tbn0.gstatic.com/i...yegzsRlsTbeSGg

I have a Janome 6600, this has the stop/start button. Silly me, I didn't take the classes or read the manual for about a year. What a pleasant surprise!:o It was so exciting, getting my new machine, that I just raced home with it & started sewing. I'm going to practice & will probably use it for FMQ, but like others, for piecing I like to use my foot pedal & keep both hands on on my fabric.

This is the way I feel about the start/stop button, too, on my Brother 450Q. I've always used a foot pedal and having to use my hand to start and stop seems like an added burden to me. I do use start/stop when I want more immediate control but normally I still use my foot.