Virtually all the musos I've played with are better at one than the other. Only half a dozen out of hundreds are genuinely good at both - sight-reading or playing by ear - which I presume your question is asking.
When we start, most of us are slightly better at one than the other, and my feeling is that that one gets favoured. That leaves the other trailing, so the one gets strengthened while the other weakens.
To the question. In certain circumstances, being able to 'read like a fish' - never understood that one - is paramount. Given a new chart, it's instantly playable, and comes to life there and then. Trouble with that is, usually, it gets played exactly as written, as the player is doing what he's told, and often can't/won't do anything else. Not knocking it. It's a fantastic skill, but for me falls a little short, as the player often doesn't put his own mark on it. Great when someone is depping in a band, as everything sounds like it does every time.
The other side of the coin is to hear something, and reproduce it. Exactly if you like, but also most of these players will change things subtly, which for me is what music is far more about. It's organic rather than clinical - for me, I emphasise. Trouble with that is, they can't do it until they've heard it. Obviously. So there's a time factor and effort factor involved. Either they have to listen to a recording, or have someone play it at the time. But after, it seems to come more alive than the previous scenario.
So, both very important, each in its own way, and somewhat subjective - which isn't popular here - and the deciding factor may well be, as David says, what each means to you. If you envisage playing in an orchestra or the pit, then the former is better. If it's a covers band, maybe the latter. If it's quality jazz, maybe both... My choice is 50/50!