According to Cambridge Police, neither brother had a gun permit:
http://www.boston.com/news/local/massachusetts/2013/04/21/ma...
Massachusetts does in fact have an assault weapon ban in place (similar to the 1994 Federal AWB), although you can get modified/MA-compliant versions of many "assault weapons" such as the AR-15/AK that are legal, however you are limited to a 10 round magazine. They would have needed a Class-A LTC to even contemplate owning such a weapon -- this involves fingerprints, a full background check, references and a "letter of purpose" along with permission from your local police chief to get.
However, the younger brother was too young to get a permit, the older brother was in fact not a US citizen and was here on a green card and thus is ineligible for a gun permit. Having said that, even if he was a US citizen his previous arrest for domestic assault would've rendered him ineligible for/and or revoked an existing LTC-A had he had one.
I have not seen anything yet reported as to what kind of long gun(s) they had or where they got them. The FBI warned agents responding to Watertown on Thursday night that they had "fully automatic AK47s" [along with grenades/dynamite and IEDs]. It is my understanding that they only recovered two handguns at the scene of the firefight in Watertown and one handgun and a long gun were found on the boat after the final surrender [aside from the IEDs scattered over Watertown].
It is interesting that despite the incredible firepower the brothers had access to (handguns, long gun(s), multiple IEDs), that when there's someone shooting back, the brothers plans were pretty much shut down and the loss of life/injury was very minimal considering the circumstances.