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The main thing about Rifts is the setting allows you to have literally anything in it. In one campaign we played we ran into Godzilla (well an egg that would have hatched into a baby Godzilla and pissed off mom but we managed to get it back first) and a crashed space hulk with space marines and genestealers.
Rifts is not really a post apocalyptic setting anymore as civilization has rebuilt itself...it's just not as nice as before.
If you want true post apocalyptic then Hell on Earth is closer
Also...Rifts is Savage Worlds on steroids. Things routinely have Toughness of more than 20 (sometimes 30) with huge damage dice. It was my group's first time in Savage Worlds so we appreciated the lower numbers of most other settings when we tried them