Now, hold up. I'm not talking about who would win in a fight (although that's also an interesting question). I just wanted to get everyone's perspective on these two awesome protagonists Nasu Kinoko wrote for the Japanese people (curse you Typemoon, think about the Westerners!) and Mirror Moon translated for us. This isn't so much about who's "better" so much as comparing and contrasting them, and what you prefer with that in mind.
First, let's see what they have in common. Both of them present themselves as these average, nice guys with really complicated family issues that they don't fully understand at the beginning of the story. Then, both of them manage to jump out of the woodwork with special abilities that no one else understands by the end of the story. They also both have a pretty similar sense of ethics, but that sort of comes with the territory of being protagonists and being written by the same author. I feel like there's more I should be saying here, but that's all that comes to mind right now.
Next, let's look at their love interests. Emiya Shirou has three love interests (albeit all well written) in Fate/stay Night, and that's about it. I can't deny that by the end of each route, I think I managed to fall in love with the characters just like Emiya did, that's how good I think they were. But then there's Shiki. This guy has seven routes to go through, not including the never released route expected in the Tsukihime remake and the other girls that still have a crush on this guy. If anyone has followed all of Shiki's stories, then you know I'm right in saying this guy is so ridiculously popular with the ladies its actually hard to swallow. By the time you've finished Melty Blood this guy has so many possible love interests you have Tenchi Muyo and every other harem anime protagonist stopping to say, "God damn Shiki, isn't that a bit much?" And while I would normally say that Emiya's love interests had more depth, by the end of each route for Tohno Shiki I found myself going, "What was I thinking? This is the girl meant for you." And then I introduce my forehead to my desk when I get back to the ending list and realize I said that five times. And after arguing it over with myself, the only one I could really cross of the list was Ciel (ahahahah, sorry ).
Then, there's character development. For what it's worth, as I see it, while Shiki has some growth, he doesn't change a whole lot by the end of his stories; his development is pretty much the same with just some differences between the two "types" of routes in Tsukhime. I guess that makes sense considering how many routes he has and how many games he manages to be in, too much drastic change would be hard to accommodate for, the main thing he does is change the lives of the girl he picks and everyone else nearby. Considering how much time we get to spend with him, it's pretty easy to relate and get attached to him.
On the other hand, I think that it's almost the reverse for Emiya and Fate/Stay Night: Shirou is molded by them, and goes through tons of development because of it. This guy comes out a new man by the end of each route, though I guess you could argue that Shirou just isn't very consistent. That said I do think he is consistently more intelligent than Tohno Shiki. Maybe that comes across as a bit harsh, but I feel like Emiya understands a lot more, sometimes coming up with analogies to better understand what's being explained, while in Tsukihime and Melty Blood we had a lot of Shiki going, "Wait, I don't understand," or someone saying, "Shiki/Tohno-kun/Nii-san, you're so dense!" for one reason or another. But maybe it's him making up for how many times he has the crap beaten out of him.
In the end, maybe I'm a bit biased for playing Fate/Stay Night first, but I like Shirou a fair bit more than Shiki. Although I do like Shiki a lot too, and I think it would be awesome for the two of them to go on an epic adventure together and have their own bromance as they try to save the world from an army of Dead Apostles and Heroic Spirits.