Lozjam
A Cool, Cool Mountain
Breath of the Wild's Link's normal running speed is that on par with TP Link's without using the Stamina.All TP Link would need to do is wear his magic armour until Breathys swords all broke then he would be able to chase breathy down who would run out of stamina during fleeing and then he would get murdered.
Plus, the Powered Up Master Sword had near unlimited stamina. Even if it broke then, Link would just have to stall for 10 minutes until sword regenerated. Which he can easily do by creating an updraft. BotW Link can also hold far more arrows than TP Link(and he has more powerful arrows to boot).
Plus, BotW Link has access to far better armor than TP Link.
The Sword also powers up when you are fighting non-Ganon controlled Guardians as well. Which leaves me to believe, that any magical energy leads to the Master Sword powering up. So when fighting another Link, I think it's pretty safe bet that the Master Sword would power up due to the presence of the other master sword.It's not that it matters what you're fighting, it matters what is near you. So for instance, if you're near a Guardian, it's going to power up because the Guardian is possessed by Ganon. Some part of him is nearby. But if you hit a Bokoblin with it, it's still going to be powered up. Also, if you're in Hyrule Castle, where you're surrounded by Ganon's evil, then it's going to stay powered up the entire time.
Plus Mipha's Grace.Meh, not really. It runs out of Rupees even when you're not taking damage. Besides, All Breathy needs to do is hit him with a shock arrow, and he'll drop all his stuff. Can't kill anything if he doesn't have a weapon.
Also, something that should really be taken into consideration is Breathy's regenerative ability. I mean, any other Link will have what? Four bottles? Six at most? Of course, one of those bottles is probably a fairy for emergencies, while the rest can be blue potions. That's all fine and dandy. But Breath of the Wild Link annihilates all other competitors when it comes to health items. Even if you only count cooked food slots (of which he has 60), and stock them with items that will fully heal Link up to his 30 heart maximum, and use each one when Link is at .5 hearts remaining (because not all Links use quarter hearts, so that is the lowest common denominator of health) then he has a total healing capacity of 1,770 hearts (29.5 x 60). On top of that, he doesn't need to sacrifice any of those slots to hold Fairies.