You're still comparing two different data structures. Is there a good hash table in Rust? If you use that instead of the B-tree, I would expect it to be at least as fast as Nim.
B-trees are especially bad for string keys, because comparisons are expensive.
EDIT: From Rust docs: "Currently, our implementation simply performs naive linear search. This provides excellent performance on small nodes of elements which are cheap to compare". (emphasis mine)