For best three years you can go either way, but Jagr's all around offense dominance lasted way longer than the window provided.
True, but outside of his best 7 dominant seasons, all of which were indeed close to his 1998-2001 level, Jagr has nothing besides the 2nd All-star team in injury-shortened 96/97 and a couple marginal top10 finishes in points.
Ovechkin, on the other hand, visibly dropped off after 2007-2010 (though even his off-peak play was enough to win Hart in 12/13 and be the best skater in 14/15) - but Ovechkin was one of the best LWs pretty much every year of his career.
Just look at their All-star team voting finishes:
Jagr 7x 1st, 1x 2nd
OV 8x 1st, 4x 2nd, 2x 3rd
and OV is not done yet.
The fact that the poll is close on a forum that is the stronghold of recency bias should tell you all you need to know. Jagr was clearly a step above(and that's not a slight towards Ovechkin there are 2, arguably 3, players who peaked higher than Jagr offensively- not counting Orr).
The close poll reflects the confusion caused by the strict comparisons of three-year peaks.
I think voters generally remember that Jagr's consecutive peak was 4 years, not 3, and that Jagr stayed at close to his peak level for 7 seasons - and since the poll asks to compare peaks, Jagr gets extra points for that despite the poll asking to compare best 3 years vs. best 3 years.
If you ask me "Did Jagr have a better peak than Ovechkin?", I would say "yes, because Jagr's peak lasted longer".
That does not mean that Ovechkin's one-year or three-year peaks were lower (they were not) or that Ovechkin's career value is lower (it is not). But using "Jagr", "Ovechkin", and "peak" in one sentence causes a knee-jerk reaction "Jagr>OV".