well i didn't cry for either, but i felt much closer to tears with sirius. but although it was sad cos DD and harry really had had a relationship over the years. sirius' was worse because their's was a budding relationship and both of them cared about each other so much. both of felt that the other was like the past brough back to life, sirius was a link to harry's dad and harry was like james for sirius. they had such a tender, budding father/brother/son relationship that it made it all the crueller when it was prematurely ended without being allowed to reach it's apex.
with DD both of them knew how the other felt so it wasn't such a blow. sirius' was definitly far worse. also for both harry and sirius it was like someone had come back from the dead for both of them they were both young and should have enjoyed so much more together. they had all these plans for the future and all their hopes were focused around each other. getting a house together etc. but it wasn't the same with DD, he was old and he had to die sometime. although it was hard to let go, it was expected.
ps- i'm heartless. it takes alot to make me cry.