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I have gotten comfortable with the time that I am at now with my beginner's method, and would like to become better. Should I learn Yau or Hoya for 4x4?

Yau. I consider it to be objectively better, but even if both methods were equally good, Yau still has more resources available (example solves, tip videos from elite cubers, reconstructions, etc).

I use Hoya because it fits my solving style, but Yau and Hoya are pretty much equal for 4x4. But like adimare said, Yau has more resources. I recommend what JAGC said, spend some time trying both, and then decide.

I've watched the first 5 minutes of a Hoya tutorial, (it's 7 minutes long), and just like @adimare says, in my recommended section I see so many more videos directed to Yau solvers. How to get sub-40 with Yau, 3-2-3 edge pairing, Yau walkthrough solves, etc. Because of @TipsterTrickster's recommendation, I began to watch a Meyer tutorial by Kian Mansour, and it said that the method was for Roux solvers.
I'll try and see a Yau tutorial tomorrow.

Yau is a more developed method, so I would just learn Yau. Also, I think it is easier to learn, Hoya seemed to have more steps when I watched a tutorial.

Yau is a more developed method, so I would just learn Yau. Also, I think it is easier to learn, Hoya seemed to have more steps when I watched a tutorial.

Anyway, I personally like Yau more, having done 20+ solves with Yau/Hoya/redux/sandwich/etc. Yau and Hoya are identical after the cross and centres are solved, so the difference lies in everything up to that point. Yau's cross edges are more efficient than Hoya's, while Hoya's centres are more efficient than Yau's. Yau has more resources available, so it'll be easier to get fast with it, but that doesn't mean it'll be a better fit for you than Hoya.

(I'm a cross/F2L-on-left person, so I can immediately transition from cross to edge pairing to F2L without z rotations, which is another bonus of using Yau, albeit one that is irrelevant to 99.9% of cubers today.)

Yau is a more developed method, so I would just learn Yau. Also, I think it is easier to learn, Hoya seemed to have more steps when I watched a tutorial.

Yau:
1) first two centers
2) first three cross edges
3) last 4 centers
4) last cross edge
The rest
Hoya:
1) first four centers
2) cross
3) last two centers
The rest
This is the way I see it

I have gotten comfortable with the time that I am at now with my beginner's method, and would like to become better. Should I learn Yau or Hoya for 4x4?

Here's the deal. They are both good methods, but Yau has much better results in terms of world records. I personally use Hoya and it is definitely a method you can get sub-40 with. However, I don't sub 30 averages are all that possible. I know Ryan has a 27 official single, but I don't know anyone else that fast with it. Yau is the main method most people use and has constant sad 30 results for the best in the world. I would learn them both and choose which method you like best. I know 5 methods on 4x4 and Hoya is my go to. It is all down to personal preference so learn as many methods as you can and chose your favorite.

Yau is a more developed method, so I would just learn Yau. Also, I think it is easier to learn, Hoya seemed to have more steps when I watched a tutorial.

Yau:
1) first two centers
2) first three cross edges
3) last 4 centers
4) last cross edge
The rest
Hoya:
1) first four centers
2) cross
3) last two centers
The rest
This is the way I see it

I used Hoya when I first learned 444. Then I played around with CN Yau for fun. I can definitely say Yau was more annoying to get comfortable with but I did better with it.

I guess if you want to call the second two centers a separate step from your first two then it’d seem to me they have the same number of steps. First four centers seems like one step to me though. You don’t even have to start with two opposite centers

I used Hoya when I first learned 444. Then I played around with CN Yau for fun. I can definitely say Yau was more annoying to get comfortable with but I did better with it.

I am not sure. I honestly prefer the RrUF F4E and L2C but I seem to do better with Yau. Well, after Jay told me about making the last edge and storing it on the R face, I did better.

I've tried both. I think Yau is more annoying to learn than Hoya. Hoya seems more natural to me and it's what I use whenever I do a 4x4 solve.
I can't say anything about actual top speed because I don't care about 4x4 average faster on megaminx and feet.