It's tough. Bang definitely has a gigantic mixup game that in my eyes outshines Nu's and Arakune's. Bang being able to jump cancel most of his normals is one, since with that we can't really IB 360/720 if they are canceling all of their normals and flying around Tager like a butterfly. The inability to properly buster hurts Tager's game already. He doesn't necessarily live on his 360s, but the fear of a 360 makes the game worse on Tager. They'll constantly stay in the air, and collider only goes so far in the game considering it has no invincibility frames.
Bang can almost never touch the ground in this fight unless Tager just backdashes for 20 seconds straight. Backdash and punish a jumping attack is probably the only good tool Tager has for this. But if the opponent knows how to bait a backdash, Tager just eats nails and a combo. If we were to take both players at the best of their abilities and fully knowing the matchup, I cannot honestly see a Tager player coming out near even with Bang. There's just too much that Bang can do for Tager to stop.
Tager in the air is dead weight since the Bang can 2D, jump cancel it if it's blocked into something else, or dash twice to be back at full screen. Bang may not be doing much damage, but he will get guaranteed hits and combos all over the place since Tager's so easy to hit for him. Tager can't block low while Bang is in the air, Tager can't block high when Bang's on the ground since his lows are much faster than his overhead, and both lead to seals and a possible Distortion.
Bang with nails on the field is even worse. Bang simply can move almost freely and tag Tager once and zoom away. Tager's only chance at catching him at this rate is to charge spark bolt and fire it as he dashes away. Oh sure, Tager mains will say backdash, but as I said earlier, a baited backdash is not good. Remember, if you think you see an attack off of a Bang dashing in the air once, and you backdash, they can dash one more time and combo off of that.
In the end of the Bang theory simply I cannot see what Tager can do against Bang's amazing pressure game when the Bang player only uses jump cancelable normals and highlow games you. I mean, if you can manage to backdash a jump in or dash in, Tager controls that with a combo or 720. Maybe tries to AA with 2A, but Bang can just jump (If they have another one left) and punish it, or empty jump and command grab because you'll be expecting that crossup.
I'm aware both Arakune and Nu have tools to bait backdashes as well, and that Nu has a great mixup game. But both shallow in comparison when we look at Tager. Which will be described below.
Nu: Ah well, no matter what I say people say Ribaia vs Galileo. That's probably the most linked to fight on this site. But in that fight Galileo did absolutely nothing but block and attempt to close the distance, when at least 3 times per round he had the option of letting Nu come to him, and him destroying Nu. Nu has those swords, we know. Nu can zone anyone out. That's true. Tager needs to get the magic distance for B sledge to be an option, and even then it might not be a good idea if the Nu is good enough.
Someone somewhere called me an idiot for saying Tager has to push Nu into a corner and Tager has instant advantage. Claiming that act pulsar gets her out for free and gives her a mixup because she can TK 2147D. Well sure. But a good Tager will stand at Act Pulsar distance, and 360 that command upon reaction. Yes, Nu actually has recovery on it. You can even 720 them if you want. At 2/3 screen Tager has control of the match if Nu is in the corner. Believe it or not, he does. Nu's only option is to keep those swords coming, in which Tager can inch forward bit by bit until Nu has to pulsar out into a 360, or IAD into the backdash 360. If not, then B sledge counterhit. Yes, even if they 5DD J.2DD 214D. If they stop doing anything, you stop doing stuff. It's that chess match where Nu gets frightened. If they don't they are overconfident. Nu has to burn 50 heat to safely get out of that corner, and give Tager close to 100. In which, Tager can start the closing in all over again.
Arakune: Sack of bugs is ridiculous, but not impossible to overcome. Will edit later. Leaving.