Does field type matter in a MongoDB index?

I don't have a specifically accurate answer on the matter, but here is my understanding:

Indexes

Indexed fields may be of any type, including (embedded) documents

Indexes are mostly likely hashed, regardless of the type, to be able to index the same way. If there were specific considerations to be observed for different types, the standard mongodb docs would make that distinction.

The answer given to a similar question here refers to code samples from mongodb, that suggests the index comparisons are pretty much the same regarding types, but probably performance geared towards the size of the index.

One thing to note about strings versus numbers when it comes to indexes is that the order for a number in a sort is generally well understood. However when you use a string Lexicographical Order will be used instead, so you need to be aware of the differences there.

Also, to follow up on the size angle mentioned by jdi, the string can be arbitrarily long, though that can be controlled of course, a long, which will be stored as the BSON double type will always be 8 bytes.