BigCommerce integration, being a recent addition, currently supports a subset of features that we support on Shopify platform. Here are the features we support on BigCommerce at present:
Opt-in prompts (Custom prompt, Browser prompt & Flyout widget)
Welcome notifications automation
Abandoned Cart Recovery automation
Segmentation (except product based condition like "Viewed a product", "Purchased a product" etc)
That said, the missing features are on our list and will land up over time.