I think, more often, the dichotomy is between idealistic designers and pragmatic designers.
Idealistic designers care about whether the end-users (meaning the people who will, say, visit the website) like the design.
Pragmatic designers care about whether the client likes the design.
It's quite a bit harder to make money as an idealistic designer, unless you can wield conversion rate data at the client. If you're just one designer on a team working for an agency, who's been given a "brand policy" document by the client? No chance.
I disagree with the your dichotomy. It isn't whether the end-user likes the design, it is whether the design is useful. So useful that they don't even realize "design" is taking place.
The good designer knows how to get the client to understand that the end-user is the one who needs to value the design :-)
[Top tip - never ask the client "What do you think of X?" instead ask "What would your customers think of X?". You'll be amazed at the different kind of responses you get.]
Idealistic designers care about whether the end-users (meaning the people who will, say, visit the website) like the design.
Pragmatic designers care about whether the client likes the design.
It's quite a bit harder to make money as an idealistic designer, unless you can wield conversion rate data at the client. If you're just one designer on a team working for an agency, who's been given a "brand policy" document by the client? No chance.