The show is fairly explicit about Walter White being an extremely gifted chemist, and only being a teacher rather than a multi millionaire because he'd left the company making money from his innovations because he was in a sulk that his co-founder was dating his ex, and he just assumed that he was going to be able to make a second multi million dollar company on his own and that his friends hadn't contributed at all.

The meth was better quality not just because he used the right equipment, but also because he put what other people considered an unreasonable amount of effort into avoiding trace contamination, and intuitively knew which unwanted reactions he needed to worry about and take measures to avoid. In a later episode, Jesse has to demonstrate how to make comparable quality meth to some professional chemists who have been failing to do so, and the only thing he can find that they've been doing wrong is not keeping things clean enough. After meticulously cleaning things that were already deemed clean, he gets something close to Walt's results.

How it was written, it came down to the care taken in the process and cleanliness of the gear being used. You can see part of this when Pinkman show the cartel their method.

I haven't watched it in years but IIRC he was kind of a genius. He founded a (medical?) research group but he left before it got successful. I think because his son was born and had special needs so he had to get a more stable income.

The friend he co-founded it with is the one who offers to pay for the treatment. He still holds Walt in high regard but Walt feels like a failure in comparison.

In addition to the cleanliness of the lab, Walter also decided to cut the pseudoephedrine from over the counter drugs out, along with the steps required to extract it from the other ingredients in the cold medicine and instead synthesised his own from methlemine.

No idea which one is easier to get a pure result from, but that was his first "level up" to the blue meth he became known for.

Though what set him and Jessie apart from Gail is hard to say, other than Walter sabotaging Gail instead of just teaching him his techniques (iirc, been a while since I saw it).

The series does seem to be taking the stance that "before Walter White, professional chemists worked for legitimate companies doing legitimate work in professional labs while drugs were made by hobbiest chemists in ad-hoc labs that were neglected even if they had professional equipment and the people running them had no idea about the single most important factor when targeting high purity: the purity of everything else along every step of the process or some way to extract purity before the end step".

He was pretty explicitly a world class research chemist. Even with a written recipe there's a lot of room for variation in chemistry and knowing what's happening is how you correct.

In earlier seasons it's because he does stuff right and uses the right tools correctly. People are impressed with his product but it's just uncommon.
In later seasons he's making industrial quantities of laboratory grade meth. A rough estimate would have his output being a serious competitor to a pharmaceutical company (walt made ~15,000 kg of meth, and the US produces about 30,000kg of amphetamine per year).

So his competition is mostly people who work for Pfizer. Similar to how most bomb makers work for national governments. The people who are good at it make more, safer, by doing it legit. It's why it's always newsworthy when a professional level player does private business.