Are there some tying methods that are more suited for thick strings over thin strings (halachically or aesthetic)?
There is no correlation that I am aware of between thick/thin sheetot and halacha/aesthetics. Some people find thick strings (regardless of sheeta) to be more aesthetically pleasing on a large talit. Some people buy thick for talit katan due to greater durability (they don’t tear as easily). I have found that thin strings tear more easily when tying the Rambam teimani tying method and thus, especially for beginners, I recommend using thick, just so one doesn’t tear the string while tying.