One of Big Mom's biggest advantages over Minato is her physicals. She is a powerhouse in terms of stats and Minato would be hardpressed in overwhelming Big Mom in this department.

To give you a baseline for how strong Big Mom is, at the age of 5, she broke the bones of a giant just by fitting his arm. And this was as a toddler!

She was even able to tank a sword slash from the strongest Giant in Elbaf before killing him by slamming him into the ground by the beard.

For reference, Hajurdin, a far weaker Giant, was able to tank several blows from and punch a ten thousand ten opponent a far distance away, so the fact that Big Mom not only blocked an attack from the STRONGEST Giant, but also one shotted him is very impressive, especially when you consider that she did it AT THE AGE OF 5 (while Hajurdin did fall unconscious, the fact that he tanked several ten thousand tonner blows before he went unconscious and the fact that Big Mom one shotted a much stronger Giant is impressive). So imagine the power that Big Mom has as an adult.

To give you an idea for how strong a fully grown up Big Mom is, without her Armament Haki, Big Mom can CASUALLY cancel out a Gear Third strike from Luffy and no sell a kick from Sanji coming from the side. And again, this was all WITHOUT Armament Haki.

For reference, Gear Third Luffy smashed through a gargantuan, thick metal door and Sanji before Diable Jambe and before he acquired Haki, was able to kick a creature hundreds of tons in weight, several feet into the air. And Big Mom canceled out both of these attacks CASUALLY, without the use of Armament Haki.

Now with Armament Haki, Big Mom is a different beast all together. She was able to casually cancel out a Kong Gun with her forearm. This doubles as a speed feat because she was able to react to a punch from Luffy, and Luffy in base form can punch lightning out of the air.

A Kong Gun from Gear 4th Luffy is easily large mountain level in attack potency. To prove it, I will quote myself from a previous opener:

Even in base form, while heavily fatigued, Luffy was capable of leveling a city block and punching through several meters of bedrock.

And keep in mind, this city block busting feat was without the use of Haki and again, Luffy wasn't in his prime, so current base form Luffy is capable of much more damage than this.

In Gear Second, Luffy was able to oneshot a Pacifista.

What makes this impressive is that a Pacifista has been shown to be able to tank blows from pre timeskip Gear Second Luffy, Zoro and Sanji.

Now, as stated previously, base Luffy has broken through bedrock, leveling a city block in the process, putting him at city block busting level at the bare minimum considering the context..

Gear Second Luffy has been described as able to push Luffy's body to its absolute limits. Considering that Luffy was in a weakened state when he did his city block busting feat (meaning he can likely do more damage in prime condition) and combined with the fact that Gear Second allows Luffy to push his body past his limits, pre time skip Luffy in Gear Second should be able to deliver a hell of a lot more damage.

Now as for Sanji and Zoro, they have both shown the strength to deflect Oars' attack.

Oars has the powers of Luffy, and his striking strength is even greater than that of Luffy given his immense size and mass. Now Oars is just as fast as Luffy, who is a casual lightning timer in base as I will get into later on. Now combine MHS + speed with strength greater than Luffy and you get a strike that is very very powerful

With that said, tanking hits from Zoro, Luffy and Sanji in rapid succession and still being able to get up from that attack easily puts the Pacifista at city level durability, making Gear Second Luffy's Pacifista busting feat city level +.

In Gear Third, Luffy was nearly able to shatter a larger than island ship beyond repair with his Elephant Gatling attack. While this may seem unimpressive, the fact that the Noah was able to no sell being 10,000 meters underwater, makes this feat the contrary. And like his base form feat, Luffy was heavily fatigued and had sustained multiple wounds when this feat was accomplished. This feat easily puts the Elephant Gatling attack at mountain level +.

Finally, we arrive at Gear 4th, Luffy's ultimate form. While Luffy has three variations of this transformation, for the purposes of this post, I will focus on Boundman as that is the form Luffy uses most often and is his goto when things get rough.

We have already established that one strike from Gear Second Luffy is city/mountain level +. Well, despite this, Doflamingo no sold a barrage of Gear Second attacks coated in Armament Haki to boot.

I can't stress enough that Doflamingo was unmoved by this attack.

So with all of this established, let us get into the most popular Gear Fourth feat: Knocking Doflamingo across multiple city blocks. Now while people may lowball this attack to multi city block level, considering that Doflamingo had no sold being bombarded with city level + attacks, I would argue that this attack is easily large mountain level as it was able to break through Doflamingo's guard with relative ease.

This all goes to show that Big Mom is CASUALLY LARGE MOUNTAIN level in durability, and theoretically in striking strength since her Armament Haki is dense enough and strong enough to cancel out an attack from Gear 4th Luffy.

And due to the fact that she matched Gear 4th's Armament Haki, we can scale her piercing durability to Luffy's with his Armament Haki. In base form and with Armament Haki, Luffy tanked a mountain level attack from Fujitora. Since Big Mom's Armament Haki is casually at the same level of Gear 4th's Armament Haki, where Luffy's Armament Haki is much stronger, Big Mom should easily have piercing durability in excess of mountain level.

As can be seen, Big Mom is called the Iron Balloon for a pretty damn good reason. She has insane striking strength and durability with her Armament Haki, both capping at large mountain level +, at least in regards to blunt force. Her piercing durability is mountain level + as well due to her at the very least possessing Haki equal to if not greater than Gear 4th Luffy. Lastly, she has an MHS + reaction speed, proving that she can easily keep up with the likes of Minato. Therefore, Big Mom has the durability to tank anything Minato can dish out, the speed to react to him, and the strength to one shot him. It really is as simple as that.

In addition to her physicals, Big Mom's greatest asset in this fight or her homies. Armed with Prometheus, Zeus and Napoleon, Big Mom becomes very versatile with her attacks to the point that she should easily be able to overwhelm Minato.

For starters, all three Homies are immortal and possess an insane, almost cartoonish healing factor.

So Minato can't do anything to damage Big Mom AND she can't do anything to damage her Homies. With that established, let us get into their abilities.

With Zeus, Big Mom can summon lightning bolts so powerful they can break apart metal.

She can also use Zeus to fly and gain increased mobility.

With Prometheus, she can literally vaporize a large part of a forest, engulfing it in flames.

With Napeloen, she can make a gargantuan sword that she can create massive shockwaves with.

But when all three Homies combine their powers, that is where they truly shine. With the combined might of her Homies, Big Mom sent Jinbe flying, overwhelming his Armament Haki.

This is impressive because Jinbe practically no sold an attack from Gear Second Luffy, which as established previously, should be in the city level ranges. And this was without Armament Haki. So A WEAKENED Big Mom forcing Jinbe to use his Armament Haki and still overwhelming him should easily put a healthy Big Mom in the city level + ballpark with this attack.