Good question. I think it might because Higuruma doesn't have the sure-hit effect that other domains possess, meaning he has greater range with the specifications for his domain. A Japanese untranslated version of a JJK chapter even stated that non-lethal domains are strong against domain clashes. Furthermore, the fact that the Jujutsu sorcerers made a back-up plan with Higuruma's domain in-mind despite knowing how powerful Sukuna and his domain are implies they believed Higuruma's domain would be enough to trap Sukuna in.
Assuming that Higuruma's domain can't prevent other domains from being activated, it would come down to which domain would win in a domain battle, and this depends on whether or not Mahito or Higuruma possesses greater skill and talent. Though both displayed remarkable feats of growth within a short time frame, I think Higuruma has greater raw talent. Higuruma created his domain immediately upon awakening, and it only took him 12 days to reach grade 1 sorcerer level. While Nanami says Mahito was born "recently", we don't know what that time frame entails. It could be several weeks, it could be a month, we don't know. He was able to learn Domain Amplification just from observing it and understanding the basics of it. His skill was enough that Sukuna himself was impressed and even asked Higuruma his name. With Mahito, however, Sukuna never displayed the same level of respect for how his abilities advanced and merely called him a puppet, implying he wasn't as impressed with Mahito.
That also reminds me that Higuruma can use domain amplification, meaning even if he did lose in a domain battle, he could protect himself from the sure-hit effect of Mahito's domain.
