OWAR
Heyward
2010: 27
2011: 0
2012: 25.7
2013: 9.3
2014: 10.3
2015: 22
signs contract and loses his swing
2016: -19.2
2017: -8.4
JBJ
2013: -4.2
2014: -24.4
2015: 6.6 (the year he had the monster 2nd half and hit like Hank Aaron)
2016: 20.0 (I think most of us thought JBJ had a great offensive season this year)
2017: -1.8
Heyward
2013: 14/67/.427
2014: 11/74/.384
2015: 13/79/.439
Prior to his new contract, Heyward was a guy that was a 10 - 20 OWAR player year in and year out. He strugged in 2011 when he was 22. JBJ was still in AA when he was 22. JBJ didn't have a positive OWAR season until he was 25. By the time Heyward was 25, he was already averaging a 14.46 OWAR per season over the previous 5 years. If JBJ was 2016 JBJ year in and year out, yes he'd be known for his bat. For their careers, JBJ has a -3.9 OWAR and Heyward has a 66.7 OWAR.
No, JBJ has not "done better than that." It's not even close.