I've done a lot of research on this subject from multiple sources. Games, print, and anime a like, most of them conflict with one another but there is a common thread amongst them. SSJ4 and Blue are different animals. Just like how SSJ4 was meant to be a different type of SSJ transformation to begin with in the first place.
Blue is the more powerful form, I'll get that out of the way right off the bat. I should say it's more inherently powerful due to the additional benefit of god ki which is on a differing level of strength from mortal ki. That being said, it doesn't come without it's downsides. Blue heavily taxes the body without proper training and causes significant stamina drain. It takes quite a long time to master the physiological changes that occur to the body when utilizing god ki and the SSJ transformation on top of it. After one is able to master the form then Blue has every added benefit that the normal SSJ transformation has, but one must still be mindful that a mortal utilizing god ki unnaturally still causes some drain.
The SSJ4 form has no real downsides at the outset. It is the Saiyan in their purest form once they learn how to harness the power of the Oozaru transformation completely. SSJ4 also has the added benefit of being great at absorbing energy of all types. As we've recently seen the Heroes promo anime, it can even harness god ki to create an extreme limit break on the form. So one must treat this transformation as highly adaptable and like a swiss army knife of sorts. It also provides the Saiyan with a huge boost in Saiya power or zenkai as they suffer damage, the Saiyan's body almost immediately adapts to new threats and as long as one can overcome them the first time, they won't have the same effect the second time around.
In closing, is SSJ4 as strong as Blue? No. Can it be? Absolutely. You just have to train yourself to get to that level of power. One might argue that it's easier to gain ground faster with a form you're able to adapt into almost immediately than mastering changes to your body and then building off that. So my vote goes to SSJ4, all day, every day.
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