If you have a straight choice between a purpose built flat and a conversion flat you're almost certainly going to be better off with the purpose built flat.
Most, though not all, purpose built flats are likely to be no more than 60 years old, whereas conversion flats are usually buildings that are 80, 100, or more years old, the flats in them are often a wierd shape, have funny little spaces that are unusable, they are likely to have poorer insulation, and may be less fire-safe than a purpose built flat - not least because many (most?) purpose built flats have solid concrete slab floors, whereas conversions have wooden floor joists.
On the other hand purpose built flats lack any character - they are often souless little boxes.