Wait this is a power debate? I'm confused. You just said just cause it's stronger doesn't mean better. However I'll treat this more like a FPSSJ(SSJ4) and USSJ(SSG) comparison.
So let's go point by point.
The way it's obtain: SSJ4 got this. Yes rare you'll get a SSJ with a tail but when the chances of getting 6 pure saiyans. When in fact 99%(Besides those outcast) of Saiyans were warriors of killers. So the way it's obtain SSJ4 also makes more sense IMO. I just didn't like the fact they pretty much gave Goku SSG. Literally gave it to him. Not even Goku liked that. I understand why they did it(For Birsu) but in general I hate you're just given the form. You could be as weak as Tarble and still get this form. So honestly I don't call it a SSJ form but rather Saiyan God form. Super Saiyan was added to seem cooler and better hype.
So SSJ4 wins this.
Now requirements. I talked about it so this will be shorter. Okay we know the odds of getting 6 pure Saiyans(Making the form more rare than a falling cow. This happen in Japan once I think.). So you're fucked if you're trying to get this. Now before anyone say the tail was cheated for Goku and Vegeta. Let's be reminded that you need SSJ. Don't forget how hard t was for them to get that. Now the same goes for any other Saiyan that has a tail.
SSJ4 wins again
Both forms surpasses all the previous form. But which one is stronger? I honestly can say I don't know. As I think with exception of fusion almost all SSJ4(s) are around the same power. I got this with Vegeta SSJ4 = Goku SSJ4. Goku could have power down or have been injured but both took damage. However the power of SSJ4 can be increased with going over the limits. Similar to SSG this needs saiyans to give you energy. However if they get into rage mode I think they an reach the same power. So I think SSJ4 has a set power that's suppose to make them the strongest in the universe by normal means. Now Super Saiyan God. Also in my opinion SSG does NOT have a set power and is based off of the energy power of the Saiyans. So in all honestly SSG is all powers compared to SSJ4. Weaker, Stronger, and Equal. I mean if the power of SSG was stronger than SSJ4's unknown power increase then would't the Pure Saiyan killed all evil saiyans instantly even with the time limit. So we can't discuss power comparison IMO. Also you keep the SSJ God power in your SSJ form if my sources are right(even though Goku most likely lost it since he used SSG twice). So The SSJ SSG power is equal to SSJ4 perhaps.
So draw.
Energy Drain time limit - Pretty much self explained. SSJ4 wins. Though SSG was most likely meant to get the job done in the goal however the time limit did mess that up up for the original SSG. For Goku since he he had SSJ. Unless he had the power in base which creates a plot hole. Saying this because the original SSG as soon as he lost the time limit he died. SSJ4 only draw-back is that if you lose energy you revert. Don't know if you can master it.
But SSJ4 wins.
Appearance - Now some people love SSG appearance, some people tolerate it(me), and others hate it. SSJ4. Some people think it looks badass(Me), other tolerate it, and other think it's stupid and should have been Yellow. Okay let me just say for everyone who said SSJ4 should have been yellow or SSG should had been a yellow SSJ4 should see what a yellow SSJ4 look like. That looks AWFUL and I mean AWFUL. IMO SSJ4 should have been Brown or Black. Okay this is not common AT ALL. But Super Saiyan God looks SCARY not cute. SCARY. I would rather fuck around with SSJ4 than SSG only because of how scary SSG look(
Chuquita is going to kill me ). Those eyes are creepy with his Golden like skin and red hair. He looks like he can mind fuck you like a Jedi, Kotoamatsukami , or his eyes are the Death notes. He looks like he can kill you in a second. SSJ4 however looks cool and a great mixture of being an ape/monkey and a human like body. So yeah. SSJ4 might look more tougher, badass, and regular,
SSG wins for looking more scary(The exact opposite of what was intended) and looking like he can fuck you up if you mess with anything he likes.
Now, I personally think SSJ4 is the overall better form and heres why. Even though SSJG is stronger and faster, the fact it cannot be obtained alone and that it has a time limit seems to be a severe disadvantage when compared to SSJ4, which has no drawbacks that I can think of. All SSJ4 has to do is outlast the time limit of SSJG and the fight would essentially be over for SSJG. Some may say that SSJ4 wouldn't last bud id like to point out that Goku survived a beating by Omega Shenron and still managed to hold the form not to mention blow Omega up to the point where he had to regenerate so I definitely think SSJ4 has the durability to outlast the time limit and the battle will be over.
You pretty much took the words right out of my head, No better way to explain this. I also don't want a power debate over Vegetto and Birsu since this have NOTHING to do with them. Vegetto isn't a SSJ4 nor a SSG.
P.S: I have to do one DBGT joke. SSJ4 only draw back is your less durability to weaker objects(But more durable to stronger objects) and your power increase but your muscle decreases.