I'm assuming that Terry doesn't have some alternate world old man Bruce Wayne in his ear the whole time and is fighting solo?
1: I give this one to Terry. Three years of experience under the cowl showed him to be lightyears ahead of where any of the Robins were at that same point in time during their tenures. Also, points go to him for having picked up the mantle right away, without the years of training that someone like Dick Grayson or Damien Wayne got whenever they became Batman in various alternate stories. Given this, I feel safe saying he can hang with prime Bruce from TAS. He knows Bruce better than arguably anyone. Has been inside his head more and has a better understanding of all his tricks and secrets.
Adding to this is the superiority of the Beyond suit, with all the advantages of the tools he needs without the burden of cumbersome attachments. Increased strength. Flight.
All in all Terry does this with very high diff. Extremely close, his advantages just slightly outweigh traditional TAS series Batman here.
Should be noted too that Terry did much more without the added help of consistent sidekicks. Dick Grayson, Tim Drake, Barbara Gordon and even Catwoman to an extent were always hanging around to lend a hand after about two seasons of the show. Terry had much less assistance, though one could say Bruce could be a substitute for this. However, I'd say it's not as important as being physically present in any given situation.
2: JLU Batman takes this one for me though. I don't know if I have as much to say on this one. My biggest reasoning would be Batman's ability to deal with planet level threats on a regular basis, having to hang with the likes of Wonder Woman, Supes, MM and so on, taking on Darkseid, gods, and alien invasions. I'll say outright I'm not as familiar with the tail end of Beyond. However, even giving Batman the crutch of having the JL around to bail him out when things turn against him, we're talking about him having to adapt all his abilities and strategies to environments far more diverse than just the back alleys of Gotham. Space. Atlantis. Volcanoes. He's managed to be invaluable in settings reserved for gods. Given all his contributions as just a wicked smart, determined and rich asshole in constantly stopping continental and planetary threats, I believe he can swing to the situation from scenario one to his advantage based upon the diversity and success of his JLU resume.
