After what seems like a lifetime of Bujinkan Ninpo/Budo Taijutsu (on and off since 1986, currently graded 2nd dan and did not exactly rush to get here), I have also been training in JKD under one of Bob Breen's black belts for a few months now.
The kind of JKD I have been doing, including full-on boxing in a boxing gym, a fair bit of judo based groundwork, plus some kali and escrima, has benefitted my taijutsu hugely, and I have taken to a lot of the JKD very quickly, especially once the distance has closed and the pre-takedown grappling is taking place.
My taijutsu is more alive, I am harder to hit and less flat footed, without compromising the movements ingrained into me over more than two decades, and whilst I am stuggling with the footwork, trapping, and Escrima stick usage as opposed to hanbojutsu/sword, it's all going well enough that I already feel I have added to the actual 'toolbox' that I would draw from in a real fight (hint: this toolbox contains no kata or rigid form, just concepts/principles that I can flexibly apply as required).
Someone said recently that sytems do not fight, martial arts do not fight, it is human bodies that fight, and whilst there will be similarities in movement between practitioners of one style/art (far more so in JKD than BJK BBT because of the total lack of control and unilateral agreement over what is the correct way to do just about anything in our vast curriculum, see various forums and youtube fo evidence of this), at the end of the day you will be doing your own version of whatever you are learning, based on your own physiology, skill, aptitude, attitude, experience etc etc and when you are fighting for real it will probably not look like anything and certainly not recogniseable as an identifiable fighting style (unless you do something theatrical before you lose your teeth and fall to the ground)
Look at the clip below:
Admittedly Dallas Ninjutsu is not pure Takamatsuden taijutsu, but it is run by an ex Bujinkan 10th dan, but the point is, (and look at all the other bouts linked to this one), can you tell which fighter is using JKD and which is using 'ninjutsu', because I certainly find it very difficult, which should really not be the case with my experience.
I can't rule out what other people have said in this thread, and I can't say how I would be getting on if I was a novice in both arts, but there is certainly no harm in cross training, in fact it is beneficial if you want to 'keep it real' and experience what might be used against you (basic Sun Tzu 101), but I do agree that you should probably have one art as your core art and add aspects from others very carefully.
But even this is difficult to justify when The Bujinkan contain 9 arts which would have been very different originally, and have very different ways of moving etc, but we are not told to concentrate on one in particular and then assimilate the others with caution, so a lot of the preceding advice flies in the face of what many of us struggle with on a daily basis. There is of course the generic art of BBT that most of us are graded in, but it is made up of so many different things that adding something like JKD to the mix is not necessarily the worst thing you could do.