Both. Many attacks take the form of an exploit to get a shell, then using available utilities to exploit the kernel to escape to the host. If your image has neither a shell nor utilities that won't get very far.
What percentage of CVEs can be used to obtain a shell, but can't otherwise be used to obtain some other form of code execution in a distro-less container?
I haven't run any stats and am certainly not an expert but I would expect quite a few. In the one scenario you merely need to pull off an exec with a valid path. In the other you need to either write a block of memory and mark it as executable or else write your payload out to disk and mark the file executable. So it's the difference between being able to pull off a single syscall versus most likely needing arbitrary code execution.
The actual attack surface of your application? Or the attack surface of you and your team's attention from a busybody security org.
It's important not to confuse the two.