One way to give continuous players and pistol starters a different experience, is to drop the "provide only ammo for weapons availiable in the map" rule that most mappers adhere to.
For instance, if map 8 has a (secret) BFG, map 9 could be a map with a challenging Cyberdemon, where you get a rocket launcher but no BFG (for pistol starters) but still have some cell ammo (for continuous players).
That way both types of players get the experience they prefer: continuous players are rewarderd for their carry-overs, while pistol-started receive a slightly more challenging "each map as its own adventure" experience.
The way I see it, that's how the IWADS were built: the rocket launcher in MAP01 or the BFG in E3M3 are useless within those levels, but come in handy in the following levels, rewarding exploration throughout levels, instead of only within them.
Off course, in that case mappers should make it clear in the .txt file that this is how it works in their wad, to avoid having pistol-starters wasting time searching for weapons which simply aren't provided in the map.