It is interesting on paper, but I wonder if people view JBJ as someone you have to platoon long term. His minor league numbers are noticeably worse vs L, and this year he had a drastic split. Last year, he murdered lefties though. Schwarber doesn't have much of a split at all in the minors but in his SSS at the major league level, he's been unserviceable vs L. His strikeout rate gives me a little pause as well, although his minor league strike out rates weren't really an issue until AAA.
I'd guess it would come down to how much value you put in defensive metrics/how much you value defense over how much you value offense. Schwarber profiles as the much better hitter. Schwarber was putting up an .842 OPS at the Major League level at age 22 in 273 PA (and a 1.017 OPS in 243 PA in AA for a perfect age/level comparison). At the same age, JBJ was putting up an .809 OPS line in Portland over the course of 271 PA (and a 1.016 in 304 PA in A+, a league he was old for as far as real prospects go). Even if you write off JBJ's 2014 as an outlier like I do, his profile doesn't compare to Schwarber's and using someones OPS at age 26 and comparing it to someone's OPS at age 22 is really missing the point.
I'd make the trade if I were the Redsox because Benintendi (or less likely, Betts) could move over to CF. I think the improvement in offense is worth the small drop off in defense. Plus the whole contract/arbitration situation. I also think JBJ will settle in as an .800-.850 OPS type bat that should be platooned versus L often in favor of Chris Young and Ben10.
There also really shouldn't be much jury out on JBJ's bat unless you view 2014 as anything more than a guy who is either called up way too early or injured. Remove 2014, and he is a model of consistency. Plus, the average AL CF slashed .261/.321/.407 last year. Bradley's 2nd half was .233/.315/.412. I'd be interested in seeing if he faced more lefties as the season went on.
His year totals vs R: .277/.363/.538 in 454 PA. Vs L: .239/.309/.356 in 181 PA. He also has significant road splits.