The three areas of northern England are distinctive with the Lake District ironically mountainous (hilly) in spite of it name (lakes). That said, the Dales are pretty hilly where walking any significant distance involves a lot of cumulative up and down. And the North York Moors are not completely flat as its name implies.
Got a chance to check my Paul Hannon Coast to Coast Walk gide.:
Lake District Patterdale to Burnbanks (over Kidty Pike) = 2700 ft iof ascent mostly in the first 5 or 6 miles of 11 miles.
North York Ingleby Cross to Clay Top Banks =2700 ft over 12 miles.
We only spent two weeks crossing north England so my weather observations are pretty anecdotal. We had pretty good mostly clear weather crossing the Lake District. The day we walked from Barrowdale to Grasmere the day was so sunny and warm that my wife tried to cut off the sleeves of her long sleeve top. On the other hand, we crossed over Kidstey Pike is a whiteout that required navigation by compass bearing until we got below cloud level. And the roughest weather day walking in wind driven heavy rain was a day in the North York walking from Clay Top Banks to Glaisdale. Our anecdotal lesson is that weather can be great (i.e. blue sky) or pretty rough anywhere in northern England.
I suppose that if I had to pick one, the Lake District is a classic and the population of walkers and tourist reflect that distinction. The Dales are just plain nice with many enjoyable walking opportunities. A friend of ours rented a house in the Dales for a month at a time during late Spring for several years running and walked with a local club. The North York is scenic and somewhat desolate in terms of other travelers and memorable in its vastness. Shorter distance wise walks in the Lake District vs. longer distance flatter walks in the Dales and Moors all though the steepest country road we walked up was in the North York with the North Sea just coming into view.
Pick any of the three and you cant go wrong. (Sorry, don't know about Bowland).