Nico was on the harder tyre during the middle of the race and soft tyres at the end of the race compared to the harder tyre that lewis was on. Nice was on the better tyre at the end of the race, however the delta was not as big in favour of the soft tyre as had been seen previously in the weekend. Closer to 0.2s per lap instead of 0.6s.
Both lewis and Nico had fresh tyres at every stop due to not having to burn through sets in qualifying, and both only 2 stopping the race, meaning 1 fresh set of softs and 1 fresh set of hards put on both. The only time both drivers would have been using used tyres was at the start of the race when both had to start on the set they used to set the fastest lap in Q2.
The tire difference was much bigger than that, there are just multiple reasons why it won't work out in race of which non applied to Rosberg.
Firstly Hamilton pitted on around lap 20 and again on lap 42 or so. Effectively every extra lap you want you've got to slow the pace on the tyre and you have to drop more time on the soft than the medium. THe longer the stint the closer the pace of different tires. Secondly Hamilton was fuel saving till what 2/3rd's of the way through that stint. Third, multiple laps he did had a 0.4second improvement, more laps 0.4 seconds faster than 0.2 then the tyre went off around the 15 lap mark and the improvements shrank and Nico was gaining on him for the last few laps.
For Rosberg, after the safety car came in there were only 10 laps to Hamilton's 21-22 laps on the tyre, that meant faster speeds and bigger delta the lower the number of laps you do, this means it was significantly about 0.4 seconds a lap faster. Hamilton doing a 22 lap stint did multiple laps 0.4 seconds faster, on higher fuel an fuel saving. Rosberg only had to do 10 laps or so with much lower fuel and with all fuel saving turned off.
Even then, he went flat out for 5 laps at least trying to pass where the advantage was even larger. He wasn't worrying about the speed in the final 5 laps of the stint, he was leaving everything on the track with those tires, everything, because if he got past the tires would have a couple laps fast enough to get a gap that he would have held on even when the tires went off.
You simply can't compare someone trying to eek out soft tyres to someone who gave absolutely no regard to the tire life for 5 laps, the difference is night and day. I would think the soft tire was likely offering 0.8-1 second advantage a lap at least under these conditions and we can see by how quickly the tire fell off exactly how much he was "using" the tire in those 5 laps.
Without the safety car if Rosberg had been on the same pace the tires would have been destroyed over 15 laps, he would have had to use a much less aggressive pace and may have approached hamilton towards the end but probably without a huge amount of advantage in tires. The safety car just allowed him to push the car maxed out and you could see easily how much advantage the tire gave him in traction out of corners and braking later in to corners.
