I trust and love Wookieepedia, generally. This is another useful case for the site.
Wookieepedia Death Star II Article
"Unlike the Empire's first Death Star, which, as a result of supply and design problems, took nineteen years to be considered an operational battlestation, this much larger Death Star took far less time, approximately two to four years, to construct. Methods of faster construction had been developed in the years since the original station's conception, added to the fact that Imperial engineers made sure to allocate enough space on the station for the maximum possible amount of self-replicating construction droids."
I still don't see the logic of how the first was made in 19 years with many resources poured into it, and its smaller size, but the second (which was much
larger) was easily over 3/5 completed by the Battle of Endor. The explanation for the "self-replicating construction droids" and the Imperial engineers' allocation hardly accounts or makes up for 15 years (benefit of the doubt, instead of saying 17, which is more ridiculous) of construction on a much smaller and simplistic scale...
Responses? I eagerly await.