This forum needs more people who have experimented more, because it does make a difference. Not much of a change in some instances, but enough that it needs to not be totally discounted.
This is all in relation to normal sized slotted filisters.
Bolts like those used on the Invader add some low end and add some thump to the pick attack. They can make a pickup tubby/thuddy in the wrong application. Unless you're going for that I wouldn't put an Invade in an LP. You can swap them for slugs or Dimarzio type set screws to tighten things up and reduce the thump.
Slugs and slug sized set screws like those used by Dimarzio in the SuperD, Super3, Evo, etc. will have more power, more midrange, and more focus than screws, less low end due to their overall length.
Hex screws, like those used by Dimarzio and BK, (and by Duncan in the Full Shred and Demon) have a sharper, more focused pick attack and generally have less low end, but that can again be attributed to the ovarall length of the screws used.
Generally, the shorter the pole piece, the less low end you will have. BK uses slotted filisters that are already much shorter than most other manufacturers, including the hex screws used by Dimarzio. So most BK, even with slotted screws, will be less bassy than nearly anything else out there, regardless of the wind. The hex screws BK uses are the same length in the newer pickups I have, but an older A-Pig I had used longer hexes that also had slightly larger diameter heads than what they are using now. This material change could be part of the supposed difference some claim between older and newer BK.
The Hex screws Duncan uses in the FS and SD are shorter still, thus how the Full Shred and Custom5 can sound like two completely different pickups but both use the exact same wind.