Assuming this was run on a 64bit system, the Rust version seems to be allocating and zeroing twice as much memory as the Go version.

edit: this has been pointed out as incorrect, Go ints are 8 bytes on 64bit systems -- thanks for the correction!

  let mut cache: Vec<usize> = (0..=target.chars().count()).collect();

which can be simplified as

  let mut cache: Vec<usize> = vec![0; target.len()];

vs

  cache := make([]int, len(target)+1)
  for i := 0; i < len(target)+1; i++ {
    cache[i] = i
  }

Rust usize being 8 bytes and Go int being 4 bytes as I understand it.

So between doing more work and worse cache usage, it wouldn't be surprising if the Rust version was slower even with the faster allocator.