I live in one of those locations (Howardian Hills and Northumberland) and constantly hanker for the other.
I know both very well, having moved north from Suffolk (commuting into London) and holidaying in the other for the last 20 years.
The Howardian Hills have the benefit of being within 30-40 mins travelling distance of York and 1hr 15mins to Harrogate. I know you have said you are looking for remote but York is a wonderful city and there is nothing more atmospheric that an evening concert at York Minster along with a meal in one of the amazing restaurants that pepper the city streets.
The Moors and coast are also relatively close (although I am not that fond of the Yorkshire coastline). The area experiences quite a lot of tourism, with honeypot towns like Helmsley, peppered with holiday cottage's and literally having dark high streets in winter. Big attractions like Castle Howard, bring lots of tourism and local jobs, but also contribute to summer traffic congestion on the A64.
When house hunting it is worth understanding the nature of house ownership in the villages. The big Estates, Castle Howard, Hovingham, Halifax etc. can own many of the properties in a village and can have a big impact when selling land, putting forward development plans etc.
Northumberland is more remote in many respects, with wonderful beaches and the beautiful Cheviots.
Although there are a number of nice towns, you do have to go to Newcastle for a city experience and it is a much larger city. Whereas I feel safe wandering around York at all times of the day and night, I don’t feel the same in Newcastle.
Tourism is also a big factor in the coastal locations and winter can be a very different experience in Northumberland once the tourists have gone and the businesses focused on serving them shut up shop for the season.
In terms of weather I feel that the Howardian Hills are warmer and dryer. Never as warm as the long dry summers of Suffolk, but actually a lot more comfortable. My experience of Northumberland is that it is cooler and wetter, particularly inland and towards the Cheviots. However, it can be a county of two weather patterns. The area around Bamburgh does seem to have a microclimate, often being warm and dry when the Cheviots are shrouded in mist.
When it comes to getting around, the bus services are much better in the Northumberland coastal belt. At least in summer. Without a car in the Howardian Hills you are pretty stuck. Train services are pretty similar, trains run from Malton and the coast into York where you can pick up the East Coast mainline north or south, along with services west to Leeds, Liverpool, etc. The same mainline serves Newcastle and then Alnmouth, Berwick etc.
£1.5m - £2m will buy you a wonderful home in either location, although I think the Howardian Hills are more expensive. Talk to Blenkin & Co for advice about the Yorkshire property market They sell a lot of properties off market and are a great York Estate Agent. I bought my house through Savilles. They do really understand the nuances of land ownership in both markets and should also be able to give you good advice.