I'm addressing different points in my response.
Should you take notes? (Short answer is yes for most subjects especially if you're new to the material and/or have terrible memory)
The long answer is it depends on the subject, individual, and level of expertise in the subject. As an example of the first, it's not uncommon in music to learn by listening so note-taking benefits are limited. For the second, some people can capture information without the need for notes but there is plenty of literature (and this has also been joked as the "Lake Wobegon" effect) that most people feel they can capture information without note-taking but when actually tested their performance was weaker. But recognize most of these studies were for people studying new subjects, which brings me to the final point. If you've been practicing the field for awhile, then the knowledge is embedded in your head so your need for note-taking is less. From experience, you know what you need to pay attention to so you may not write it down. As an example, I've worked with two world leaders in their respective domains. I rarely saw them taking notes when it came down to their own fields but for new materials they did: one was biochemical engineering (expertise thermodynamics) and the other was statistics (expertise biochemical engineering).
What does the science say about note-taking?
It's actually quite complicated for a variety of reasons but here's a short synopsis. First, most people don't know how to take notes and there have been studies on people learning from their own notes vs. those provided by the professors. People did better with the latter but considering that doesn't
happen most of the time I consider it a moot point. But if you can get lecture notes from the source use them.
Second, science has actually looked at listening vs. taking notes (and not reviewing- called encoding) vs. storage (which is reviewing notes either you've taken or provided by the expert) and there are many papers that
talk about it but one pretty good review paper is by Kenneth Kiewra (1989) Review of Note-Taking: The Encoding-Storage Paradigm and Beyond). Below is a relevant excerpt
From Kiewra's paper:
"In 61 studies reviewed by Hartley (1983) and/or Kiewra (1985a), 35 found facilitative encoding effects, 23 indicated that note-takers and listeners did not differ significantly on performance tests, and three studies reported that listening without note-taking led to better performance than note-taking. Among studies comparing the storage and encoding functions, the storage function has proven more beneficial (e.g., Carter and Van Matre, 1975; Fisher and Harris, 1973; Kiewra, 1985b; Rickards and Friedman, 1978)." [Complication was that testing immediately after lecture revealed in many cases no difference but after waiting a week or longer after the lecture the note-takers/reviewers often did better. So, for most realistic settings either take or review your notes. Cramming is not recommended]
What's the best note-taking technique?
People state Cornell but the reality is unless you review, reflect, and synthesize your notes it doesn't matter which approach you take. Cornell just makes it easier to do those steps but the others can be modified to do the same.
Now in the words of one of my professors, "You are not asking the right question."
If the objective is to learn, then note-taking is one way to do that and is the preferred route for most topics and beginners (aka students). But it is not the only way, deliberate practice which may or may not include note-taking is a more general strategy for acquiring expertise. K. Anders Ericsson published a layman's book on it called Peak: Secrets from the New Science of Expertise if you want to learn more. (But even his research has its critics)