What is the most recent comparison of signature files and inverted indices?
Don't know any fresh references.

Off the top of my head:

Signature files require candidate verification via forward files. This requires lots of random accesses, basically one per potential match. One random memory access is 100+ CPU cycles. You can do a lot of work in 100 CPU cycles (e.g., you can decompress more than 100 IDs single core http://boytsov.info/pubs/simdcompressionarxiv.pdf). 

Random access speed is even worse in the case of HDD or even SSD. There is in fact a growing gap between random and sequential access speed.

Before making this random access you cannot do pruning, early-termination, etc... BTW, for the most fancy recent data structure, you should probably check partitioned Elias-Fano indices:
http://pages.di.unipi.it/rossano/wp-content/uploads/sites/7/2015/11/sigir14.pdf