Genshin Impact’s gacha system has a handful of “pity” mechanics that guarantee characters at certain rates. Understanding these is what you would need to know if you want to consider a 10 pull vs single pulls.
The first pity is the 4 star pity. You are going to have at least one 4 star in every ten wishes you make on any given banner. If it is an event banner (which use Intertwined Fates) there is a 50% chance this 4 star will be either an advertised weapon or character, depending on the banner.
The second pity is the 5 star pity. This one guarantees a 5 star within 90 wishes. Like the 4 star pity, this one has a 50% chance of being an advertised character or weapon in an event banner.
Both of the above pity counters are reset if you manage to randomly get a 4 or 5 star, respectively.
Likewise, the event banners will guarantee an advertised character or weapon within 2 rolls of their rarity level. This means that if you fail the 50% chance of whatever was advertised, the next time you get to have an item of that rarity level it is guaranteed guaranteed be an advertised one.
All pity counter are held over between banners of the sake event.
Using myself as an example: last month had Kazuha as an event 5 star character. During his banner, I randomly got a Mona, which is also a 5 star but not the advertised one. This means that, from the moment I got Mona, I was no more than 90 wishes away from getting Kazuha. I still failed to get Kazuha during his month, but managed to make 40 wishes after Mona. We are now in an Ayaka banner, so if I can make 50 or more wishes, I would be guaranteed to get her. If I fail to make 50 wishes, Yoimiya is the next event character banner and my pity counter would carry over to her, and so on.
Dataminers have also found there is a hidden pity mechanic not advertised. This one raises the rate of getting a 5 star when your pity reaches 70, maxing out at 75 and continuing until the 90. This maxes out at roughly 20%, significantly higher than the 1.6% chance normally.
All of this adds up to: both 10 pulls and single wishes are just as likely to result in a high rarity character. If you desire a specific character, it is more important to know if they are on the event banner or not, or if they will he in the future. Once your pity reaches 70, it is often advised to use only single pulls to make sure you don’t “waste” wishes that could be used for something else, as you may draw an event 5 star earlier and using single pulls gives you a chance to stop once you get who you want while a 10 pull will keep going until all ten are used.