The service of the Conrad Tokyo is one of the best I’ve ever experienced. If someone wants to see or to get reminded, how good services at a hotel can be, the Conrad is the right choice. I’m looking forward for my next stay.
But you can’t do anything wrong with the Hilton. Less points and a better location for your plans are very good arguments.
But: Most of the time the availability of standard room awards is better at the Hilton. So it is easier to switch an standard award stay from Conrad to Hilton than from Hilton to Conrad.