Sure there is a difference. My experience is primarily with alnico 5 rods, but blades, pole pieces, bar magnets and the like all have different sounds. First off, you need to seperate things that direct (I'm sure there's a better term for this) magnetic energy, from things that are magnets.
Most (I'm pretty sure there are a couple of exceptions) blade style pickups are using the blade to direct a magnetic field thats provided by a seperate magnet, (once again other guys might be more savvy about this than me) where as the "regular" pick-ups you alluded to (p+J) use rod shapped magnets. These are generalizations, as there are some notable exceptions here too. Some manufacturers use bar magnets and what appear to be rod style magnets are actually just slugs, that like the blade style pick-ups you mentioned direct the magnetic field.
so... without going too much deeper into this, they all sound different because the way they sense your strings is different. Considering that even different types of alnico 2,3,5 and 8 can sound different with all other variables the same, you can expect that differnt types of pick-ups with dramatically different magnets, pole pieces, bobbin construction, wind and wiring are going to be very different.
If you are looking for a better comparison, it might be cool to limit this to a comparison between some specific types of pick-ups.