What brand of food processors & blenders are used by professional cooks ?

I use a Vitamix. It's perfect because I have 2 sizes of jars that I can use for small or large jobs. I used to have Viking appliances, but have been phasing them out since that company was sold.

I agree with Pierino - Vitamix and food processor. Mine is a Cuisinart and has stood up for years. The Vitamix is expensive until you remember how long it lasts.

For an hand blender, Robot Coupe is good, but costs the same as a small car.

Hobart is the brand you will find in professional kitchens.
Hobart used to make KitchenAid, but sold that division many years ago and today KitchenAid uses plastic gears instead of metal.
Look for a brand that is made with a metal body, has enough weight to not bounce around your counter top, a metal gear box. Wattage is not that important for home use, 300 watts is just as efficient at home as 1,000 watts in a restaurant.
If you are serious, go to a restaurant supply store and find a small Hobart. It will still be in good running order when you will it to your grandchildren !

I think VitaMix is the "go-to" blender, but it's pretty expensive for home use if all you're going to do is smoothies and the occasional recipe. I love my Breville Hemisphere blender and it's about half the price of a VitaMix. As to food processors, I have a sort of vague idea that America's Test Kitchen's tests found that one of the major brands didn't hold up very well in the long run, so you might check their site for more details.

Robot coupe is what I've always used in restaurants- crazy powerful and durable. And totally unnecessary for home use. I think they're extremely pricey also (as in over $800). At home I use a cuisinart food processor and I love it. I'm note entirely sure which model/capacity I have, but it has a very heavy base (most important part), a few different bowl options, and it came with a dough blade. As far as I know all of their "top of the line" processors are excellent.