I see them as addressing separate issues.
They overlap in that they both address the notion of how to access attributes in some sense, but really they are complementary techniques.
HList as used by OOHaskell provides you with a mechanism by which you can define extensible records and structural subtyping.
Functional references let you both read and write 'attributes' in a structure. These can be chained to access members of members.
These techniques can be used together to get extensible records that have settable fields in the form of functional references, where these references can be chained together.
HList/OOHaskell doesn't concern itself with the 'deep reference' problem, and functional references do not concern themselves directly with extensible records.
-Edward Kmett