It's sad, but most of my friends saw TDK first, and then Batman Begins.
For me, watching BB first was only an accident, because that time I was 14, I barely cared for movies at all, especially Nolan, whom I didn't know at the time. But I saw that there's a movie with Batman, and lot of people said it's great, so why not, give it a go. I watched it, and I don't remember loving it, I mean loving it like a nuclear explosion or a joygasm, you know. I "only" liked it, and thus went to watch it again in the theatres, so I saw it twice. Then came The Prestige
and I fell in love with Nolan. By the time TDK came out I was crazy as hell, and when I watched it in the cinema... now THAT was a nuclear explosion.
But I can understand why some people watched TDK first. It had great, truly huge hype around it, and everyone heard about it who loved movies even just a little. I have at least three friends who got knowledge about BB's existence exclusively from me
A bit sad, because definitely this wasn't Nolan's purpose, to watch them in the wrong order. It gives a hugely different experience which wasn't intended at all. The perspective is intentionally exaggerated in TDK, and it's a natural thing (thing's growing with time), so watching it the other way around may give you a wrong impression about the whole Batman-franchise Nolan created.