Hi Andy,
I don't know about Jazzmaster, but on my Rickenbacker 340/6 I use both Thomastik-Infeld and Pyramids, and they both deliver a fantastic vintage sound. The main difference between them is that TI are low tension and Pyramids are high tension (although still not as high as D'Addario Chromes). So, comparing the same gauge, TI's would probably give the feel of being lighter strings and would be easier for bending. Pyramids are great for hitting strings hard because they give better resistance to the pick.
The question of tension is a problem for Rickenbacker guitars because they have a rather sensitive neck and some people have reported that Pyramid strings have warped or even broken Rick necks, especially where the neck fuses with the headstock, which is the neck's weakest spot. This why they are no longer so popular among Rick players and have been replaced mainly by Thomastik. However, I do not think that string tension would be a problem for Fender bolt-on necks, and therefore choosing between these two flatwounds would only be a matter of playing preference.
But, perhaps you should also look into compressed strings (also called ground wound or half wound strings). Here is what it says about them in Wikipedia: "cross between roundwound and flatwound. Such strings are usually made by winding round wire around a round or hex core first, then polishing, grinding (thus the name, ground wound) or pressing the exterior part of the winding until it is practically flat. This results in the flat, comfortable playing feel of flatwounds, along with less squeaking, without sacrificing the tonal characteristics that come with roundwounds. The polishing process removes almost half of the winding wire's mass, thus, to compensate for it, manufacturers use winding wire of a heavier gauge. The strings because of the less material, usually have a raised price compared to flat or round wound."
Factory Rickenbackers come with these compressed strings (made by Rickenbacker) and they sound very good. The only reason I have stopped using them is because they are unavailable where I live, but I would definitrely recommend that you try them.
I hope this helps.
Cheers,
Bojan