Batman
This model will always be my favourite thing to use in BMG and my main Batman since 1st edition. The consistency he had as a brawler is something I have always been a big fan of, and it has only improved with the changes to 3rd edition. He is tanky with the split of stun and blood damage, his blocks are very consistent now against all but the toughest beaters and ignoring strength dice entirely while he can punch back very well. Effectively getting 6 attacks dealing double stun, 5 of those with rerolls and the other one always on a 3+ means he will be fairly easily knocking out enemy models (great to combo with cops for the new 3VP Arrest objective). All in all he's a good Batman in the fight both offensively and defensively, and is well worth his cost for what he brings as a key piece in the crew.
Sure Nightwing is a good fighting model with his great statline for 90 rep, but his potential as an objective runner is far better. He can potentially move 19" and Manipulate or Attack if he has Audacity (Move+Batclaw+Tactical) which is really good for his flexibility and potential to score VP wherever it's needed. He also has Acrobat and Jump Up to help him defensively which is a great thing to have (as guns will be the premiere way to shut off manipulators, cancelling shots is huge). It's expensive to hire him for this role but you get a lot more out of using him as a combined attack/objective piece when and where you need him instead of just a pure attack model.
See also- Hawkman- Hawkman occupies a similar role with his flight, just with more melee punch, less native speed and no gun defences.
Knightfall
Batman
My other favourite “Batman” is quite different in terms of playstyle to Batfleck, being more of a scalpel and outright aggression piece. Knightfall Batman is less murderous than in 2nd edition with his blood/stun weapons being less effective, but he still keeps most of what he did in being Fast, +1 to hit in melee with possibly being hard to block (Unstoppable, which he should be doing whenever he doesn’t Batclaw) and Sturdy letting him always Effort the maximum amount regardless of damage. His flamethrower is still hilarious fun and effective and Medium Armour protects him far more than before against damage, just removing 2 attack dice every time he is targeted by enemies (making him all but immune to attack/RoF 3 and actually immune to anything below)
Captain
Cold
Another model who was decent before, Captain Cold is now a complete powerhouse. Adding both a Resource Point and +1 to initiative rolls, plus the free Manipulates that come from Order, plus also having a Beam weapon at +2 to hit with possible 6 blood. What more could you want for his cost? He also has Teamwork with Heatwave for in Team Arrow and Freeze crews, and Leadership is decent when it matters. Cold is slightly easier to knock out than he was before, but at the same time damage is split now so he’s harder in that regard as well. 
Captain
Boomerang (Suicide Squad)
Still the simple piece he always was and really didn't change in any significant way, but where he did change is really useful. Greed now lets him only score Objective Cards that don't involve killing, which opens up a lot more options than existed before for him in getting VP and although he won't be wanting to kill models he can still definitely soften them up for something else to score (and blood/stun helps here because he won't overdo one of them). Elusive also changed into something very useful in that it lets him always effort to make an opponent reroll an attack die of any ranged attack against him, which is helpful in almost every case because 1 stun is better than whatever damage he would take normally. Not always going to work in his favour given his defence value, but it’s a chance that you should be willing to take. 
Misc
Black
Manta
For a model that has long been really quite crap, Manta has improved significantly with the changes of 3rd edition. The biggest change is to his offensive abilities as he effectively doubles his Death Ray’s usefulness with the strength die being an extra shot (and through Beam ignoring cover, so it’s getting the 2 shots often) and through his melee being fairly consistent now at landing damage (although at blood/stun he’s not fantastic at taking them out solo). His biggest trick is through Amphibious as he can pop through sewers, straight away shoot his Death Ray in its effective range (or just use Night Vision and take the dice loss) and land big damage on models without any chance of them mitigating the threat through their own movement and then being straight in the action. Otherwise with Stealth and Bulletproof Vest he is lasting against guns, he gives extra Resource Points and Persuasive is always good to mess with an opponent’s plans (especially in forcing models without Audacity to activate so you can mess with them more)
This one is pretty simple, they lost their one major weakness (Just A Scratch whittling them down) and gained a huge bonus (all enemy attacks lose 2 dice every time they attack). Lex remains a primarily control based piece, but denying Special Actions is now such a huge thing that an Intimidate in the right place can be game changing. The biggest downside for Lex is only getting a single Special Action himself, because Fly, Unstoppable, Goad and Intimidate are all excellent and he can only use one on any given turn. As for the crew they still work like before in that they are very elite, although they lost the Jetpack equipment for gaining Accurate (which is still amazing on the Heavy Trooper)
Ra's al Ghul and League in general
Really I only want to mention this because he
rerolls his Crit:Casualty now and I love that. With it being his only special
action, you will always do it when he has Audacity, but the amount that he
brings in terms of support is still really good like I mentioned with Cold
above and the same as Lex. Cancelling opponent’s resources, giving himself
extra Resource Points and +1 to Take the Lead rolls go a long way in dictating
the game and being a defence 5 Martial Artist also means he will be hard to
remove (and if they do, they can’t score off it). His combat still has +1 to
hit and rerolls the strength die, but with the downside of losing a dice if he
attacks things cheaper than himself (so go after expensive models with that
crit and have a blast!)
League as a crew got a big buff in that they
don’t need to roll wound rolls any more, and still get rerolls on everything
else. They will shred henchmen now (hopefully they get some more kill
specific cards) and can do some really good combat lists that aren’t easily
shot at. They can easily adapt to the marker based game with the movement and denial tricks they have already, and once they get their own deck they will be a force to be reckoned with for sure.
