Here is my own, personal guess at what things would look like had Boeing been selected as the JSF prime contractor. This is from a programmatic point of view, not an airframe point of view (because no one really knows a ton about what Boeing would have built because it was significantly different than what they actually tested because Pentagon requirements changes).

Boeing's attempts to reduce structural complexity through the use of large single piece thermoplastics would likely have continued to give them fits for years. They surely would have figured it out eventually, but not until they A) had significant problems in fabrication, and problems with finished units developing cracks from previously unseen flaws, and B) become the world's greatest experts at constructing aircraft from thermoplastics, which is a really cool thing to be good at.

Their direct lift system would have been the focus of much, much testing, even more than the F-35, because there's a corner of the STOVL envelope where their direct lift is significantly more dangerous than the LiftSystem concept.

How their software development would have progressed is much murkier because software is so complex.

They likely would have received the same incorrect wire dynamics model that Lockheed got for the F-35C. Causing significant delays in testing of CV.

In short, a continuation of the issues you can see in the "Battle of the X-Planes" documentary plus a repeat of some of the same mistakes on the F-35 plus some unforseen stuff that you never know about until you test (structural resonance issues? flutter issues? fatigue cracks? performance problems?).

Anyone who thinks it would have been better without qualification is fooling themselves. Some things would have been a little better, some would have been a little worse, one or two things would be far better, another couple would be far worse. Overall it would all be a wash, I think.