As the prince, He can't just merely side with either. It isn't a matter of not wanting to chose, It's a matter of Irene has dirt that can ruin the whole empire. He can't show favoritism towards either Regina because it's a fair fight. Irene has been using the dirt on him constantly to try and force him yet, Sadie is the one he loves so he's pushing away from Irene. It isn't like he doesn't need to think about how to chose. It has to be as fair as possible. All of what's happening so far are all of the competitions. Like the hunting, The trips, The territory management contest, And so on. These are all things that they do to prove themselves as worthy to be Empress. I don't understand why you'd think he is letting them do all the work. He literally can't get involved. Sure, He can comfort them from the shadows but he can't publicly show his support for either one or the empress will consider it an unfair fight and accuse Sadie of seducing him or such. His job is to make his judgement all throughout the competitions. And, He isn't even the one deciding. Whoever completes and wins the more challenges will be Empress. It's as simple as that.
I feel like the prince is letting both girls do all the hard work so that he doesn't need to think about who to choose.