From what I know of them from reading car magazines and forums (not actually driven one)...
The supercharged one is, as you know the previous model, with a Chrysler engine, the new one, the turbo, uses the same lump as the 207 GTI. The old one is often reported to have better build quality than the new one. I had heard that BMW actually over-engineered the first one and made very little money on it. Once it was established on the market and the successor came out, it was built more to a price.
I've also heard people say the previous model is slightly more fun on the handling too, with the newer one seeming more "grown up" somehow. Obviously having never driven to compare, I dont know how this pans out in reality.
The supercharged model has that whine, which is absent from the turbo model. Whether you like it is up to you but its obviously quite distinctive. The supercharged lump is likely to be slightly crisper responding at any given revs because of the nature of supercharged engines.
That said, the supercharged lump apparently has a very linear delivery, which can make it seem somewhat underwhelming according to some, and apparently the performance is not brilliant, particularly in 163 bhp form. Its also rather thirsty and will be liable to higher tax than the new turbo model...
The turbo model on the other hand, although lacking the whine of the supercharged model, is actually a technically better engine, which produces far superior emissions and fuel economy, 40 MPG is no great difficulty in the turbo whereas the SC model struggles to break 30 according to many owners. Not only that but the Peugeot turbo lump is very strong indeed as standard, and its rumoured that it kicks out a bit more than claimed power.
As a result the turbo model turns in far quicker acceleration figures, and in fact is allegedly not too far off the pace of the supercharged Cooper S Works model, which has a fair bit more power on paper.
Personally although not a fan of either, I personally prefer the looks of the older model. The new one does seem to "look" cheaper and not quite as polished as the older one. I've been less than impressed for example, with the huge silencer on the exhaust of the new one which looks like a cheap aftermarket stainless steel exhaust thats just been whacked on with little consideration for the design, and the car seems to look somewhat akward to me from some angles.
Supercharged one will lose less in depreciation and likely wont go wrong, so that probably makes up for the higher tax and lower MPG. Newer one will have warranty available, be faster out of the box, but perhaps not quite with the "character" of the older one, but will cost more to buy.