I've played around with a Friend's Phonobox and it is a very good phono stage at the price.
But it's not so much that the MM input is better than the MC input, but the internal transformers are not particularly good. Using a good external SUT with the MM input will produce much better results with an MC cartridge. I used an EAR MC4 (as does the friend who loaned me the unit) which is a significant upgrade (although it does effectively double the price of the phono stage).
But your Grado Sonata2 looks like it needs a 47k loading, so using a SUT is probably not ideal for it, even though it has low output. Going directly into the MM input probably would sound better for that cartridge, assuming you can get sufficient gain, which appears to be the case from your comments.
If using an MC cartridge with the EAR Phonobox (or Phono Classic in the US) better results can be obtained with a good external SUT. It can also be improved significantly by switching it internally to work with 12AX7s, instead of the less common tubes it ships with. Current production Tung Sol 12AX7s are inexpensive and are an excellent upgrade for the phono stage.