You're comparing apples and oranges- the two are in no way alike. And it really depends what you want from a holiday.
If you want to potter around and go to tourist sites and tearooms then go to Northumberland. The castles are great and the Holy Island etc are lovely. It's also decent for bike riding and sea swimming.
If you're into fell running, watersports, or walking, it has to be the Lakes. It's the most beautiful part of the country imo and the experiences you can have there are incredible. Obviously Bowness and Ambleside are touristy hellholes at peak times, but they're not the best spots for walking, swimming, running etc anyway. I go to the Lakes several times a year and don't go anywhere near those places, so genuinely don't view it as a "busy" place to be. Happily, the tourists have little original thinking so all stick in the same spots!