Research shows that breastfeeding mums both get MORE sleep than formula feeding mums, but also BETTER quality sleep, and report feeling more rested.
But, I think this relates to the newborn period, and not necessarily to the older baby period. And I also suspect that STTN isn't as common amongst BFing older babies or toddlers.
Having said which, I think dealing with night wakings is infinetly easier with a BF baby. As you can simply roll over and feed without waking yourself properly, it's often not such a faff dealing with night waking. I'd find it really hard to wake myself up, go and prepare a bottle, while keeping baby from waking the household. Breastfeeding had a 100% success rate for getting baby back to sleep - and worked great for toddler too - and enabled me to rest while I did it and everyone else slept on. And the sleepy hormones BF produces meant I went back to sleep too.
Yes, I'd rather that my BF toddlers hadn't woken. But seeing as they had - and many do, including FF ones - it was SO EASY to breastfeed them to sleep!!!
So I suspect that BFing means better sleep, esp in the newborn period, for mums. And it makes dealing with night waking easier. But your specific question about STTN: I suspect not.