Quite a lot.
I don't know too many pickups exactly the same but with bar vs pole, but for a close comparison look to Deluxe minis vs Firebird......or a neck p90 vs the 54 custom staple pickup........or maybe even a clip of a wide-range humbucker vs the Fender repro.
It's going to depend on many factors but to be REALLY overly broad, in a Fender-style single coil with magnet pole pieces, I tend to get a fuller sound and louder output with greater clarity and string detail, compared to the same pickup with steel slugs over a bar magnet. Much of that is likely due to the closer proximity of the magnet to the strings, as well as a tighter magnetic field. There's also the permeability of the magnet vs steel poles and the greater amount of ferrous material with steel slugs and a bar magnet.
It's very hard to make such a broad prediction though, when there are so many other variables. I should also mention that I think most designs where you see Fender type single coils with steel pole pieces, they are made as adjustable steel screws set between two small ceramic bar magnets with opposing poles, similar to a P-90 configuration. Comparing those to a typical AlNiCo Strat pickup is like comparing Apple computers and Orange amplifiers.
FWIW - I rather like dual slug humbuckers with magnets as pole pieces, with or without a steel keeper between them.
Mine? On Fender singles? More ferric mass, more non-permeable material, wider magnetic fields. If those are good things or bad things is really up to your guitar/rig/pickup/ears. I'll say this though - best to have a separate ground lead for them and keep them electrically isolated from the pole pieces.