I wonder how is the performance comparison between the two? And can I use bun parser as a drop in replacement for esbuild?

ESbuild is much more mature than bun. The author of ESbuild cares a lot about compatibility with other bundlers and stability. Moreover it is already insanely fast. I am not sure there is any interest to switch from ESbuild to bun for bundling or transpiling code.

By the way, I think that bun does not apply the patches of ESbuild since the translation date.