I not only played FF1 when it first came out for the NES, but I actually beat it. That may not sound like much, but it was a hard game, I was only 5-6 years old at the time, and there was no internet to help out at the time. Frankly, I am not so sure that if I were to play that original NES version for the first time today, that I could make it all the way through it. I sure as heck wouldn't be able to do so without looking at a FAQ a few times. It's amazing what kids can do.
I picked up the PSP version when that came out, and as someone who loved the original, I say it's quite nice. The difficulty has been decreased drastically; if it were say an 8/10 before, the new one would be a 2/10. A couple of the new additions at the end can prove a little tough, but the game itself is cake. That's not a terrible thing or anything - I'm just noting that this is a very easy RPG. The actual gameplay is more or less the same, so remember that despite the graphical niceness, you're playing a game from the late 80s. I'm not sure someone who has no nostalgia for the original game would enjoy it all that much.