Brush Pixelization Help?

We need to see the brush preset to understand what might be going on.  Unless it is a hard round brush with no scatter or random size dynamics, then how are we going to understand the resulting brush strokes?

You could maybe have a look at cache levels in Preferences > Performance, but I don't think the sort of pixelated effect having cache levels set to 1, is what is happening here.

The other thing is, to make sure you are using the brush and not the pencil, or that the Image Mode is not set to bitmap

[EDIT]   Just read your post again, and I see you are using a Cintiq.  We sometimes see issues with Wacam drivers for some Cintiq models, but I would have thought that Lazy Nezumi would iron those out.  LNP usually = nice brush strokes

I did try out Paint Tool Sai and it was smooth but I want to stick to Photoshop since I'm more familiar with it

A couple of ideas about gritty looking lines on your display:

• Depending on the video hardware, the version of Photoshop, and the performance settings, when zooming out the artwork may look gritty due to Photoshop having to interpolate pixels at an odd zoom level like 33.3%. In particular when "use Graphics Processor" is turned off, this WILL occur.
• In my experience Photoshop, even when the Graphics Processor option is enabled, the anti-aliasing of line art at odd zoom levels is reasonable, but leaves something to be desired. In particular at very low zoom levels thin lines just disintegrate in Photoshop's view.

Why your lines look wobbly/unrefined:

• Practice - plain and simple. It takes more of an effort to draw smooth strokes with a graphics tablet. Heck, I know - took me a while to get used to it.
• HOWEVER! Most painting applications offer some kind of built-in stroke stabilizer. This is a HUGE time saver, and allows the artist to draw very smooth looking line art. The problem is: unfortunately Photoshop does not offer a stroke stabilizer out-of-the-box. Photoshop (in my opinion) also doesn't have the proper 'drawing feel' that I do experience in alternative drawing software (see below).
• Stroke stabilizers are generally the key ingredient in achieving those beautiful smooth strokes. Do not underestimate experience with drawing on a graphics tablet, though. I found that taping a piece of drawing paper over my Wacom Pro surface really helps my line art. And I prefer the feel of paper as opposed to the sandy Wacom surface (and it saves nibs).

To solve your unrefined looking strokes, you have several options:

• Install Lazy Nezumi. Not free, but sort-of essential to have when drawing in Photoshop nowadays.
  https://lazynezumi.com/​
• Keep practicing those lines.
• Switch to (an) alternative(s). That is what I did for my digital drawing and painting - I left Photoshop behind for this type of work. I use both ClipStudio Paint and Krita. Krita is an open source and free digital painting alternative that is arguably miles ahead of Photoshop to draw and paint with, because that is its singular purpose. The on-screen anti-aliasing of your line art is much better, and it offers essential tools like a stroke stabilizer, a mirror tool while drawing, perspective tools while drawing, and the ability to quickly flip your artwork to check for left/right handedness. https://krita.org/en/​
  ClipStudio Paint's drawing feel is also hard to beat. A stroke stabilizer is built-in. Not free, though. I use both apps for my digital art.

Up to you! If you prefer Photoshop for drawing and working in, then I urge you to invest some money in Lazy Nezumi.

Hello, what magnifications are used in the various images?

Also, can you post help>System Info (or Photoshop>System Info on a Mac), so that we can see if you are running the latest display driver?