Recurly and Chargebee are both subscription billing engines. WooCommerce is the storefront. The question is which engine you already run—not whether Woo Subscriptions should duplicate it.
Choose Recurly Integration
Use Recurly Integration if your plans, dunning, and invoices already live in Recurly. Recurly.js sits on Woo checkout. Saving a Recurly Subscription product creates the Recurly plan. Docs: Recurly Integration documentation.
Choose Chargebee Integration
Use Chargebee Integration if billing is Chargebee Catalog 2.0. Chargebee.js (or hosted checkout) runs on Woo. Saving a product creates the item and item price. Docs: Chargebee Integration documentation.
Both plugins are $29/month or $249/year, one site per subscription, 30-day refunds. They are not interchangeable: Recurly Integration talks to Recurly; Chargebee Integration talks to Chargebee.