I get this question a lot. Bottom line answer: nothing and everything. Everything does something good. Nothing is going to do exactly what you want it to do every time. More often than not it simply a need for a new technique rather than a new product. Most of us have the bathroom fully stocked with an array of products swearing to fulfill our hopes and dreams. When they don't our hunt continues. Desperate to find that miracle product that will solve all hair problems. These do and don't exist. It all depends on your hair needs.
If you don't know what your hair needs then make an appointment and ask. Or be happy that you are already happy with your hair and don't create a problem where there might not be one.
If you do know what your hair needs are, professional grade might not be what you need. Not all professional brands are awesome just like not all drug store brands are awful. It all just depends. And it is highly up to opinions and preferences. My least favorite professional brand is Paul Mitchell. But I still buy their Skinny Serum and use it on almost every single blowout I do. Paul Mitchell is a very popular brand. Tons and tons of professionals love it and use it every day. Its just not one of my favorites. Now, on the flip side is TIGI Bedhead. That is my favorite line. However I do not buy the whole line. Not every product they make is great or better than others. Its simply my favorite because it has more of my favorite products than other lines. And lots of great smells. Don't dismiss the need for good smelling hair.
Drug store brands are not evil. There is a lot of opinions out there about "sulfides" "parabens" and other official sounding things. It all boils down to what you are starting off with and what you what to finish with. If your goals are not so complicated then don't complicate them with fancy packaging and lists of promises. However, pay attention. Drug store brands tend to be cheaper because they use cheaper ingredients. If you already have fragile or damaged hair drug store brands might make the problem worse. I don't think drug stores brands will or do cause problems, but they can make them worse.
When looking for a new product start by taking inventory of what you already have. Try using them different ways. With wetter hair. With drier hair. With a comb. With your fingers. More of it. Less of it. More often. Less often. Look up a youtube video for that specific product. Chances are you already have what you are looking for. Maybe you need an additional product instead of a different one. That is another difference between The Salon and the bathroom at home. Generally, I use at least 2 products on everyone when styling. Maybe you need to add a pre or post styling product.
So to sum up, what is the best? Anything. If used for the right thing, the right way. Any product can be exactly what someone needs it to be.