Here are some key differences between Nolan's and Snyder's Batman.
- Nolan's Batman is anti-gun. He didn't use guns to kill bad guys. IIRC, he didn't kill any. In case of Snyder's Batman, it's opposite. We can see him using guns when he tries to kill Superman.
- We see many gadgets used by both versions of Batman, but Snyder's Batman got more sophisticated and more high-tech gadgets. You can also see that suit of Snyder's Batman is different.
- That well where young Bruce fell in was behind Wayne Mansion, but in BvS, it is somewhere else. Same goes for graves of Bruce's parents.
Nolan's Batman retired first and then came back, but it is not shown in BvS because it is set many years later than Nolan's Dark Knight trilogy.
Besides this, Gordan, who was a recurring character in Nolan's Dark Knight trilogy, doesn't appear in BvS.
But (Credits to @AnkitSharma) J.K. Simmons is selected for this role which means this character will appear in future films. There is also robin costume in Batcave with joker graffiti on it and in Suicide Squad, it was clear that it belongs to dead robin. So this Snyder's Batman also had sidekick in past which was not in Nolan's Batman except John Blake.