I am hosting a Next.js project at Vercel. I write my API's in Next.js which get hosted as serverless functions on Vercel. What are the differences between Vercel serverless functions and Supabase edge functions?

You can use both/either but you may have preferences one way or the other. Vercel is more robust as their functions is in beta stage ( we are still in alpha/experimental stage). Other differences are: we require the use of Deno to create and deploy. The limitations for the edge functions varies significantly as well: Supabase Edge Func limitations: https://supabase.com/docs/guides/functions#limitations Vercel Edge Func limitations: https://vercel.com/docs/concepts/functions/edge-functions/edge-functions-limitations