It has always been my understanding that the only benefit of having a player on the 60 day DL as opposed to the 15 day DL is that a player on the 60 day DL did not count against the 40-man roster limit. As the post form MrWorkrate indicates, the language does not sepcify which version of the DL a player is on.
Also keep in mind that major leaguers are often moved to the 60 day DL from the 15 day DL on a rather frequent basis to open up a spot on the 40-man. There would need to be language to deal with accrual of service time if it changed under that scenario and there isn't.
Finally, I can't imagine the union would ever agree that a player on the 60 day DL did not accumulate service time. Can you imagine the posible abuse by franchises who didn't want to los their superstar to free agency at the end of the season?