Again I'm assuming you're talking about a Les Paul. The tonal distinction comes from the body shape and wood type, that's just for starters. Bolt on vs. set neck are also huge contributing factors. Very little to none of the tonal distinction are a result of the pick-ups, beyond the fact that the Gibson's PAFs are gonna sound much fuller and warmer overdriven.
The strat, in my opinion has a very distinct tone, mostly due to the alder body. Beyond this, Saying "Gibson" is a little bit vague to me. you're comparing a specific Fender guitar model, the Stratocaster, with a company that produces guitars - Gibson. The tonal difference between a Gibson SG and a Gibson ES-335 is extreme. What are you really trying to accomplish?
That bell like tone you speak of is mostly a result of the mahogany as a body wood, the top wood, usually maple (strats don't have a top), and the set neck, which provides a lot of the guitar's sustain.
If you're looking for a harmonious marriage of Fender and Gibson attributes, a 72' Telecaster might suit you a lot better than dropping a set of humbuckers into a Strat, (that's almost a joke), but then again it'll be more expensive too.
If you'rereally just trying to beef up your Strat's overdriven tone, dropping a set of humbuckers like the Lace Sensors or even Seymour Duncan Hot Rails will get you closer to the tone your looking for, but you're not gonna' get the tone of a Les Paul outta the deal, which is ok. In the long run your shoulder will thank you.