Looking purely at the rates on the comparison page for HR Waikiki and HP Waikiki for the same week, HR appears to be $39 cheaper for a standard room.
Once you click on each property, you see the following note for HR...
Beginning January 2, 2015, the daily $25 + tax resort fee will be $30.00 + tax per night for all new reservations made. The fee will be added to your daily rate and includes: 2 bottles of water, internet access, complimentary photo keepsake, in-room safe, complimentary local, 1-800 and International calls (up to 60 minutes) per stay, local newspaper (Monday-Friday) pick-up at the front desk, complimentary incoming faxes, Health Club access, resort cultural activities and access to beach amenities.
So HR is only $9 cheaper than HP. It's amusing that the resort fee is $5 more in 2015 as it no longer includes internet access since it's free.
For a less hectic environment, would HP be a better choice? I don't plan to spent much time on the property as I plan to explore the island in a rental.