As I described in an earlier post about the differences in neck and bridge pickup position sound, the mix of harmonics from the string that the pickup "sees" is a major driver of the difference between neck and bridge pickup sound. That said, manufacturers also tend to wind neck and bridge pickups differently, even of the same model. They do this partially to compensate/account for the different harmonic mix and output levels the pickups see, and partially because there is now a norm that the guitar is usually set up for the bridge pickup to be more of a drive/lead/solo sound, and the neck pickup to be more of a clean/rhythm sound.
So what is the difference? Generally, all else being equal (magnet choice/strength, wire, bobbins, etc.) the bridge pickup is going to be wound hotter (more turns) than the neck pickup. This increases overall output (compensates for the reduced fundamental output the bridge sees and allows for a hotter output for soloing) and reduces the frequency of the pickup's resonance (makes the pickup less sensitive to higher frequencies/harmonics, and so sound more "dark" to compensate for the large amount of higher harmonics/frequencies the bridge pickup "sees"). Exactly how much hotter the pickup is wound is to the taste of the manufacturer - these can come in anywhere from roughly equal output to the neck pickup to significantly higher output, so make sure to read reviews if you are trying to balance output. Note that even if you get a pair of pickups with significantly different output, you can always change pickup height vs. the strings to get more in the ballpark of what you are looking for output-wise, though there may be a change in tone from changing pickup height which you should listen for as well. Looking at the different DC resistances (sometimes called "DCR") of pickups of the same model is one way to know roughly how much hotter one is wound vs. another. DCR is a pretty blunt tool when trying to figure out a pickup's sound, however, so I'd instead encourage you to try to get information on overall output level, resonance frequency, and height of resonance peak (all info we should have here relatively soon, but some of which is spread around on manufacturer websites).
Using neck pickups in the bridge position and vice-versa: A neck pickup in the bridge position is going to sound much brighter than the pickup would in the neck position, and may sound much brighter than any bridge pickup you've heard before. This is again because of the harmonic/frequency mix the bridge position "sees". In the same way, a bridge pickup in the neck position is going to be much darker than that same pickup in the bridge position, and likely darker than most neck pickups you would have heard. In general I'd be careful about buying pickups for the "wrong" position without trying it out first with pickups you have around, or buying something that you would use in the future anyways (e.g. buying a SD '59 neck for a future guitar and trying it in the bridge of a current guitar for kicks).
The only other thing to note here is that for the bridge position pickup you may need a Trembucker or "F-spaced" pickup (wider pole spacing) vs. a normal humbucker size.