If you want to increase working memory (WM) capacity, then sticking to
Dual-N-Back and getting to higher levels will do just fine.
However, if you seek to increase the "quality" or "resolution" of your current WM capacity (e.g. how many tiny details you can remember in every memory item), then Quad-N-Back will get you there over time.
Some quick math for the rationale:
1. Say you can do Quad-6-Back. According to most internet views, this means that you can hold 24 items of information in WM (6 times 4 = 24).
2. Let's say the average person's WM capacity is around 7 items (+/- 2 items per standard deviation).
3. This means that 7 items = 0 standard deviations from the mean. Therefore, 9 items = +1 SD, 11 items = +2 SD, 13 items = +3 SD, 15 items = +4 SD, 17 items = +5 SD, 19 items = +6 SD, etc.
4. We know that only 0.000000099% of data will fall at or above 6 SD from the mean. This is 1 in 1 billion.
5. summary: This means a person who can do Quad-6-Back is one of 8 people on earth have a WM capacity this large.
6. In my time, I've heard way more than 8 people on the internet claim Quad-N-Back levels above 6. A prominent Youtuber has even shown his 3-year progress towards Quad-8-Back.
7. conclusion: It is statistically impossible that Quad-N-Back at higher levels is increasing WM capacity that much. People are most probably training task-specific strategies at that point and not WM.
takeaway:
If you want a quantity increase in WM, take Dual-N-Back as far up as you can go. Just avoid using strategies that merely increase N-Back level but decrease cognitive load on your WM.
If you want to make your existing working memory "high definition" (in the words of those who've done Quad-N-Back for years), then use Quad-N-Back for a long time.
Take care.