Welcome to the FT forum!! I'll give a more general comment on how I would make this decision.

Generally through studying this forum over the years I learned to see points as currency which can be traded. The key metric redemption rate in cents per point, taking a baseline of the fully flexible rate including all taxes and fees and dividing by the nightly points rate. That gives a cents/point rate. The 5th night free deal on a standard room is usually the best redemption rate. Many sites "value" HH points at around 0.4-0.5 cents per point. However I try to get 0.65 for personal redemptions. More than this used to be quite easy but isn't now although actually Edinburgh may be an exception.

Lets say I have 200,000 points in my account, the "value" of those points in USD would be $1000.

So in order to make this decision I would not consider the hotel itself but the redemption on the nights I want to stay. That way hotels of different categories (in Edinburgh the Hamptons, DTs, Hilton or WA) can be directly compared, as can different cities or countries where the cash price will be vastly different. Glasgow is a much cheaper city that Edinburgh for hotels for instance.

If the redemption rate in c/p is approximately equal then my decision making would be the hotel itself and the total number of points I have available to me to use and future plans for using these points. In practice this often means I select a lower category hotel (say a HGI) because the total number of points needed will be lower and thus I can use the balance for something else. But bear in mind that HH points always deflate in value so hoarding points is not recommended.

Edinburgh is extremely expensive for hotels especially during the summer and over the new years holiday but TBH most of the year it is eye watering. A tourist tax is coming (I think next year) as Edinburgh has become really overcrowded.