As I said, I haven`t done this analysis. I`d be amazed if the results indicated that Jagr wasn`t better at ES or Crosby on the PP. Still, it would show if the ice time argument has any merit, or it Jagr is still comfortably ahead.
Prepare to be amazed. I have the data, and I can assure you that the ice time argument has merit. Jagr is not comfortably ahead of Crosby in anything, at least not post-1997-98. We don't know what his per-minutes rates were prior to that, but Sidney Crosby is pretty easily a more efficient scorer than post-1997-98 Jagr both at even strength and on the power play. I'll use the points/60 metric since that seems to be the generally preferred one in the stats community at the moment, and here are the overall and peak numbers for both guys since 1997-98 (excluding late career Jagr since that's an unfair comparison):
Jagr Total ('97-98 to '06-07): 2.96 ESP/60, 5.29 PPP/60
Peak Jagr ('97-98 to '00-01): 3.29 ESP/60, 5.21 PPP/60
Crosby Total ('05-06 to '14-15): 3.21 ESP/60, 6.31 PPP/60
Peak Crosby ('09-10 to '12-13): 3.85 ESP/60, 5.58 PPP/60
Crosby had a higher even strength points scoring rate over his entire peak stretch (180 straight games) than Jagr did in his single best season (3.74, 1999-00). It's often overlooked because Crosby played partial seasons and did a lot of his damage on the power play over the rest of his career, but in those 180 games Crosby scored 183 even strength points, which is a remarkable total given his ice time and overall league scoring.
Unsurprisingly, Crosby was lapping the rest of the league in that metric. Here's 5-on-5 points/60 from War-on-Ice (slightly different than the above numbers which are NHL.com's even strength totals including 4-on-4 and 3-on-3) from 2009-10 to 2012-13:
1. Crosby, 3.83
2. H. Sedin, 2.90
3. D. Sedin, 2.87
4. Malkin, 2.61
5. Stamkos, 2.56
I don't have all the figures for everyone in the league in 1997-98 to 2000-01 to compare with Jagr, but I do know that Sundin scored 2.84 ESP/60 and Sakic came in at 2.72, which means that Jagr's lead over the rest of the league was much smaller than Crosby's comparing peak to peak.
Peak Crosby also had a higher power play points per minute rate than any of Jagr's seasons in Pittsburgh, even though Crosby's had the lowest power play scoring rates of his entire career in 2009-10 and 2010-11. Overall, Crosby's power play scoring rates are much better than Jagr's.
As you can also quickly see from the above numbers, Jagr's peak scoring rates for the most part (i.e. other than '99-00) weren't huge outliers compared to what he was putting up in New York and even in the first little while in Washington. When you adjust for scoring level they do stand out a bit more, but the biggest difference seems to be that Jagr had huge ice time when he was winning Art Rosses. To me, the evidence suggests that 2001-02 Jagr was pretty much the same guy as he was in Pittsburgh, just used in a slightly different way by a coach that actually rolled his lines and shared the power play ice time around, and the sulking and disinterest didn't really kick in and start really affecting Jagr's numbers until 2002-03 and especially 2003-04.
As QPQ's numbers showed, in any given season even during Jagr's peak he was often challenged by other skaters in points per minute. Over several seasons combined Jagr would generally have an edge because he was always near the top of the league, but there were often other skaters that were not very far off. For example, from 1997-98 to 2006-07 Peter Forsberg was at 2.88 ESP/60 and 6.39 PPP/60. Given equivalent ice time, that actually beats Jagr over the same period.
There's something to be said for Jagr's ability to play that many minutes, of course, and during his Art Ross years in Pittsburgh he was certainly an all-time great even strength scorer. That said, I'd take peak Crosby over peak Jagr. I'm not even sure that Jagr was really that far ahead of guys like Forsberg or Sakic, it just looks that way when all you care about is regular season point totals without adjusting for usage and role. And if peak Jagr was playing in today's league with shorter shifts and lower TOI for top forwards? I think the closest he came in his prime to that type of system was in Washington, where one of his seasons is eerily similar to Crosby's Art Ross year from last year in terms of ice time per game:
Jaromir Jagr, 2001-02: 17:09 ES, 0:14 SH, 4:18 PP, 21:42 TOT
Sidney Crosby, 2013-14: 17:10 ES, 0:30 SH, 4:17 PP, 21:58 TOT
Plug in Jagr's peak scoring rates to that ice time and you get 108 points per 82 games. Sounds about right to me.