You shouldn't be struggling much with zoning in the neutral game lol
Batgirl has SLOWER, LESS-RANGED footsie tools. Don't dismissively say "Joker has d2", it can be cancelled into gun dash cancel on both hit (for a conversion, no matter what the damage, and possibly even an oki/teeth setup afterwards) and on block to make it safe.
In general though Joker's air normals are better is all I'm saying
Teleport is still takes 20+ frames to hit and is roughly -20 on block though. True though that teeth isn't the best move in the game but crowbar is alright for an advancing special since it's safe on block and gives you oki/an otg on hit. Also true, she can punish dashes with one of her 50/50 options, b1 is helpful there moreso though since b2 has little range.
You have plus frames to work with in your neutral game that we don't though. Every option we have is either punishable, backdashable or negative. Even redemption (bf3) is interruptable for full combo even though it's +1 on block. Cartwheel, though advancing, is punishable no matter what option (refer to PLs video on how to block it and although he says "I'll just take the damage" low cartwheel is fuzziable at 18 frames of startup and -9 on block)
Your jump normals are better, you can get in with not so much risk with j3 into a mixup/setup whereas we have to make a good read to get in or we get punished no matter what we try. That's not to say that I think your neutral is so much better I just think that at least you have an option with minimal risk you can use to get in.
Gun dash cancels are uber punishable on block and only net you a conversion of about 15% on hit, with techroll escaping any setup, unless you are near a BGB.
Yeah... so don't teleport willie nillie. Sonicfox stopped doing it, and look what happened. You have a punishable teleport? Use it as a tool to punish unsafe zoning/interactable rather than just spamming it. Problem solved.
Joker actually can't punish Cartwheel if I remember correctly. At -9, we have nothing that reaches at the range that it spaces us out to on block.
Like Vengence said, all we have on the ground that's safe is ending things in flower, which is easy enough to block confirm into in regular strings and puts us at advantage, but has to just be a read off of d2, in which case it generally whiffs if d2 hits, and if you're using it against people on block, you aren't really gaining anything unless they are in the corner and you are spacing them out. D2 teeth, d2 crowbar, d2 gun dash cancel, and d2 canister are all punishable on reaction on block. So I have to rely entirely on unsafe reads in an attempt to blow you up for 15%? Cool.
What the hell are you talking about Batgirl doesn't have anything safe... her 50/50 options are -2 and -6 on block, i.e. safe as shit. And lead to a vortex. A meterless vortex. That has good wall carry. Where she does 50%+ or 40% into more vortex. Having to block a followup doesn't make something unsafe, it means you have to block a followup. That's called "playing fighting games". Stop it.
If you let Joker jump around, he can cause problems and get setups going even on block (though, not against batgirl because her small hitbox causes whiff issues that negate this tech). Even still, you make it sound like he has 50/50's after you block a ji3. He doesn't. He can do b1 (low), crowbar (overhead, 20+ frames), various strings (all mid), or b2 (overhead, 20+ frames, pointless knockback move outside of specific setups). Block low, react if you see something other than b1.
If it try to pull the gun out against you, you hold down, then I have to try to guess when you're gonna jump and go for the teleport. If I guess right, I get 8%. If I guess wrong, vortex city.
Joker's gun is like this in many matchups. Aside it whiffing on some of the dumbest things in the game (Batman's FUCKING FORWARD DASH for instance), it's got hella recovery and can be whiff punished by many zoning heavy characters as long as they wait and simply react to the shot, as well as batgirl with teleport. What? Try using canisters to zone? Oh that's true, I think the one that I started throwing in training just now might finish the animation sometime a few minutes after I finish this post, so I'll get back to you on how effective that is.
Everything Joker does to get close to someone requires a ton of risk with little reward. That is why he is a bad character. Once he is in, he can get a decent amount of stuff going if you're in the corner, near a BGB, or in some other precarious situation that I can exploit to pressure you and open you up, but otherwise you have to make a mistake for Joker to catch you.
So, I'm gonna go ahead and disagree with you. Again. Batgirl's neutral is not as difficult as Joker's. To say otherwise is just...