BBC Sherlock takes it via being physically as skilled as trained soldiers and being as skilled if not more so than the OG Sherlock with firearms. Plus Sherlock with his weaponry is quicker and better than OG Sherlock on the draw.
And to be honest, BBC Sherlock has better intelligence feats too, such as simulating in his own mind multiple days of a case he has limited information on all within 5 minutes and then simulating what everyone would say after waking up too.
Then Sherlock also has the learning feat, where Microft said he learned a Language in an hour and Sherlock called him slow.
Then there was Eureos’ puzzle, where Microft and more had many many years to figure out her riddle and after picking up the case again after 1 day figured it out.
Then on top of this was able to predict Watson and multiple other people up to 3 weeks ahead of time.
Then the bullet feat, where Sherlock was shot, before he even moved from the impact Sherlock had simulated other people and learned of what to do, how to stop himself from dying and so on all within what can only be a millisecond.
Then there was the fragment of the code, where Irene had a fragment of computer code that had been encrypted so well the top cryptographer in the Country couldn’t crack it, yet Sherlock after 5 seconds decrypted it, completed the entire code and was able to figure out what plane, when, where, and who’d be on it.