Chargebee sits between your product and your payment gateway, managing what makes subscriptions hard: plan catalogs, upgrades and proration, coupons, trials, dunning for failed payments, invoicing, taxes and revenue recognition. It works over Stripe and other gateways rather than replacing them.
It suits SaaS businesses whose pricing has outgrown a few simple plans. Early-stage products do fine on raw Stripe Billing; merchant-of-record needs point to Paddle instead.