OK, first of all, for listening, here’s my theory. It’s not based on research, just on my experience:
I think listening at full speed while still trying to understand whatever you can trains your ear to pick apart the language on the fly. It teaches you how to break down what you hear. Studying words though, especially while playing the audio again, teaches you what to look out for, and helps you recognise what you hear. Case in point: after months of listening to anime every day, and often falling asleep halfway through an episode (that wasn’t planned… I was just trying to squeeze a bit of anime into my schedule), I started the Tobira textbook, which was made for the old JLPT 2 (current JLPT N3-N2). I found myself very often able to follow what was going on in a text by listening to recordings even when my eyes and mouth couldn’t recognise and pronounce the words on the page as quickly. Also, I found that I was able to break down the syllables I heard quite accurately even if I didn’t know what they meant. As such… I guess I’d say both ‘extensive listening’ and ‘intensive listening’ are important, because it seems they train different skills.
In my opinion, anything that widens your vocabulary will improve your listening provided you know how those words are pronounced. In that sense, intensive listening is faster because it produces immediate results: by learning words that you couldn’t break down or couldn’t understand, you immediately increase your ability to understand those words. On the other hand, extensive listening may not widen your vocabulary, especially if your comprehension is low, but it may produce global results since it’ll probably make you better at deciphering words in general. I guess you should emphasise one or the other based on your current weaknesses. If your vocabulary is too small to understand more than, say, 10% of what you’re listening to, and you foresee yourself listening to similar content in future (e.g. you’re watching a drama series or you like gaming videos), it may be more profitable to do more intensive listening because you’re likely to hear the same words again. On the other hand, if your vocabulary seems fairly wide relative to the scope of your content, then extensive listening will be more productive.
Slightly off-topic comments on language learning in general
I personally don't do much research on 'the best' or 'the fastest/most efficient approach' because I found a language self-study publisher whose approach changed my life while I was learning French. Ever since, I've just tried to replicate their methods for other languages, because it worked for me.
The publisher is called Assimil, and their courses are used by Prof. Alexander Arguelles, an American linguistics professor who is fluent in at least 30 languages. He has a lot of videos on how he approaches language learning, so you might want to take a look. (NB: their Japanese course for English speakers only goes up to A2 in the CEFR. For French speakers, it goes up to B2. No advanced courses right now.)
Anyway, I’m not here to advertise, but I just wanna give you an idea of what their course did for me, and then I’ll explain their approach. You can take what you want from it. Before I started their course, my level in French was B1-B2 (i.e. intermediate learner fluent enough for rudimentary daily conversation and reading simple texts, but unable to handle newspapers or technical vocabulary. Also completely unable to handle full-speed native speech.) I was doing French as a school subject with other students around the same level as me. When I finally got their course, it took me about 3 months to finish, but even after just one month, advanced French was easy. Everyone else was struggling because we were trying to transition from the B tier (intermediate, good enough for basic general daily conversation) to the C tier (advanced, able to read newspapers and handle some technical vocabulary), and the problem with that is that the C1 and C2 levels are extremely broad in any language. You only get there by knowing lots of words from all major domains that the language deals with, which means tons of vocabulary acquisition.
So what’s their approach? Well, I’m having trouble replicating it perfectly on my own because they worked with parallel translations: target language on the left, translation on the right. You can’t always find those in real life. Also, they tend to break down sentences using additional literal translations. The idea is to give the learner natural text that could have been produced by a native, along with recordings, and then let him learn from context with explanations so the complicated stuff doesn’t make him get stuck. Of course, the texts are arranged so they get progressively more difficult, which is something we can’t always do ourselves. This is the way a typical lesson went for me:
- Listen to the text once without looking at it, just to get a feel of the language
- Listen again while reading to understand
- Read the text again while checking the explanations
- Listen a final time while trying to understand, and possibly while trying to read along at the same speed.
My approximation of their methods in real life, since I can't replicate them exactly. This focuses on what I do for listening. I'll briefly summarise what I do for reading as well afterwards.
- Watch an anime episode with English subtitles, only referring to them when needed and while trying to catch the words used.
- Watch it again while looking up words that interest me and possibly referring to a transcription
- Watch it again just for fun without subtitles
I’m currently somewhere in between steps 2 and 3 right now, because I’m watching without subtitles, but with a transcription somewhere else in case I can’t understand. Obviously, I don’t rewatch the entire episode three times in a row, because that gets boring, but I’ll probably come back to the same anime a while later.
At the same time, I try to find other material to read in order to continue widening my vocabulary. It can be a fairly advanced textbook like Tobira, or NHK news articles with help from TangoRisto or Japanese.io for kanji readings. That helps my listening too: every time I come back to a particular anime after a few weeks/months while doing other reading/watching, I find I understand more.
Finally, my main tool for language learning, concrete skill-focused methods aside: I read the dictionary a lot.
What allowed my fluency to skyrocket for French, aside from finding a really good, intuitive course, was that I aimed to transition from an EN-FR dictionary to a monolingual French dictionary ASAP. I’m currently doing the same for Japanese. The simple reason is that it forces you think in Japanese instead of in English while learning new words, and it gives you extra reading practice. Plus, if there’s a word you don’t know in the definition, you’re forced to learn it too, so you acquire vocabulary even faster. Also, most good dictionaries list expressions and common structures in the entries for each word, so you get to learn idioms and grammar too. I still use my EN-JP dictionary a fair bit (it contains more proverbs anyway), but I try to give the Japanese dictionary priority because of all these benefits.