I have a BJ4 WE and is a VERY capable car. They actually aren't as similar as you would think. Practically none of the chassis parts transfer over. I think its pretty well established that the B44 tends to steer a little more (from what i have seen) while the Bj4 seems to have a bit more rear bite.
It also seems that with the quality control of Thunder Tiger there are "good" and "bad" B44s out. Its hit or miss what you wind up with. You could have 2 b44s with the exact same setup and they would feel totally different. I don't think BJ4s differ that much from car to car.
While the B44 is a great car, at $350 I wouldn't hesitate for a second to recommend a Bj4. Still a contender. Also, its the Special Edition which is $350. You get a set of Jconcepts SAE tools with tool bag, white Jconcepts ball cups, raised front spring cups and a sealed box cover signed by Ryan Cavalieri (if that means something to you)--I think its kind of cool. And not for nothing, the quality is on a different level between the 2 cars. I don't even run my BJ4 anymore really but its a great car. I bought a SE about 6 months ago for $475, I think for $350 between this and the b44 I would go with the BJ4 we SE.