Steve Harris is a little misleading in that list, since he essentially uses a new set of flatwounds every day. They'll sound fairly bright when fresh - needed for that rollicking tone of Maiden's - so my hunch is that he prefers flats for his fingers and to reduce rubbing string noises, allowing his gallop and fretnoise to define the tone.
As for me - I'm experimenting with all kinds of strings at the moment. I like the feel of flats and for some music I dig the thump they give you, but I have a feeling I'm going to settle in on being a half-rounds guy since I prefer a little extra zing available to me and I can't afford a new set of strings every day like Harris. They're not as good at either extreme of the tonal range as rounds or flats are, but my sound needs don't go to those extremes anyways and I can truly dial in any sound I need with half wounds (or ground wounds, depending on whose doing the talking). The flat surface also keeps string noise to a minimum.
They key is to experiment, and if need be, get a few different sets. This can be expensive when buying new, so check out the classifieds on here where guys are selling or trading strings for this exact reason. Last week I bought four sets for $25, which is essentially four for the price of one.