I don't agree with your view that only Sealdah Rajdhani should be called the proper Kolkata Rajdhani because people from south Kolkata find HWH convenient rather than going to crowded north Sealdah to board train and HWH is largest serving station for Kolkata. Neither do I agree with the view that Hwh Rajdhani is better than SDAH Rajdhani, not necessarily.
Because their quality of service, coaches etc. seem to get swapped often. Just a few months back I found SDAH Rajdhani had better service but recently it seems HWH Raj has it better.
Punctuality...
more... wise, 12301 has a slight edge over 12313 but most likely because of ease of entering platform as it is the first of the whole Rajdhani gang but otherwise, both can delayed equally if there is problem in intermediate route. But in reverse direction, records show 12314 having slightly better punctuality than 12302 in last 1 year.
In 12314, the second longest non-stop stretch after NDLS-CNB is CNB-MGS which is around 350 km (skipping ALD) but in 12302/1 the second longest non-stop stretch is HWH-DHN which is just 265 km. This may make 12314 better for some railfans.
To conclude,I consider both of them to be par based on my experience on any of the factors considered.