This dichotomy seems to permeate every media, but lately I've heard it more and more in the realm of video games. The argument takes many sides, and thankfully the wide market can often accommodate both in other forms...sci-fi fans have hard sci-fi for those who want scientific accuracy and soft sci-fi for those more interested in the fantasy or philosophical. In video games, the prohibitive cost of triple A titles tends to mean that they are rarer and the variation more sparse.
I don't think it's a black and white issue, but personally I tend to find myself on the side of fun over realism in most cases. Battlefield 3 would have an entirely different feel if players had to lay on the ground and bleed to death while shouting in pain...realistic perhaps, but not all that fun. The same could be said of escort quests in games. Bioshock Infinite and The Last of Us would be substantially less fun if the people you were escorting were easily killed by enemies. Mainly this is because AI for friendlies is notoriously simple and stupid. Having these two characters be essentially invincible means the player doesn't have to babysit them and does not randomly lose because the AI decided to make a poor decision.
In my experience with Bioshock Infinite, while occasionally Elizabeth would hide in a strange place or teleport in an odd way (such as appearing behind me when moments ago she was in front) it was generally unintrusive and most of the time never broke my immersion; not nearly as much as the frustration of watching her die because the AI decided taking cover behind a lamp-post was a good idea.
Other players disagree and it's their right to do so, but a video game to me is meant to be a facsimile of reality, not a perfect recreation. Surely to, the level of reality/fun I prefer will change based on the genre. I liked the level of realism in DayZ generally; that they wanted to keep survival poignant. For that game it worked, and I am glad of it. Fun and realism also don't have to be at odds, and in cases like DayZ, realism can lead to fun...if handled properly. That is where it really matters, where the fun and realism cooperate to create an engaging and immersing experience.
I'd love to see a market that allows for more of the other, but I find that the "fun" crowd is also more the majority, which is why games with harsher rules and more "realistic" sets tend to be minority (such as EVE's hard-core economics), or ARMA's smaller community when set aside Call of Duty of Battlefield. Thus the triple A crowd lately differs to the "fun" community, and often leaves the realism side as a more vocal minority that justifiably feels overlooked.