I have stayed in both, the quality of Conrad is better and the rooms/suites are very modern and nice. The breakfast is way better. The only advantages of the hilton is the central lication close to Taksim by walk and the lounge location and views.
I think the lounges at both are closed though, and not sure what they offer instead, its worth calling them to verify.
Having said all that, my personal preference is Bomonti, I have been getting the best treatment than any other hotel I have ever stayed in for years now. The lounge views at Bomonti are on the top best you can even imagine.
Enjoy Istanbul and say Hi 🤩🤩