I think the simple answer is better footballers and more of them but there's obviously a bit more to it than that. Under Rodgers, mainly in 12/13 and 14/15, it was stop Suarez and then later Sturridge or Coutinho and you stop Liverpool.
In Klopp's first year to 18 months it wasn't necessarily always a case of us struggling to break teams down. We had a few results against lesser sides where we scored once or twice in a game at home but still failed to win. I can think of a few 2-2 draws and a 2-3 defeat to Swansea off the top of my head.
Alisson and Van Dijk have changed everything for this side. You never felt confident that we'd keep clean sheets before those two and we no longer have to score 3+ to guarantee a win. The options off the bench or when we make a few changes are obviously also much better now too.
With a stronger defence and midfield now too we've seen Klopp go with a 4-2-3-1 quite often this season to fit Shaqiri in which obviously helps our attacking options but hasn't taken much away from the defensive solidity.