I'm right at the end of Act 1.
So far the layout for Act 1 is exactly the same as vanilla LOD. In version 7.61 the levels and dungeons were re-arranged with new bosses, layouts, mappings, etc.
Andariel's Lair (cat 4) is unchanged for 7.61, this is vastly different from vanilla.
The Butcher is available on cat 4, if you want a difference from vanilla go talk to him. So is King Leoric accepting appointments for conversations, his office is on Cat 4.
There was a 7.61 King Leoric and The Butcher encounter in the jails or caatacombs, these are gone.
Act 1 differences from Vanilla LOD are the same in 7.61 as 7.69; the underground tunnels are direct portals to other areas. 7.61 to 7.69 differences include the placement of BloodRaven and Rakenishu. The Inner Sancturary map is the same, the monster population is different.
I think act 2 is the same as 7.61 (Lazarus and Creeping Feature being non-vanilla, you must collect the 5 words to cube the horadric staff)
Act 3 differs: the Durance 2 wp is gone, (remember to get the 3 words for cubing the Kalim's Will) so you have to go from Travincal to Mephisto in one run.
Act 4 differs: the 5 seals of Diablo are re-arranged: 3 where you remember them in the Sanctuary, one by the Hellforge and one by Izual.
I'm so far removed from Vanilla LOD that my answer is really sparse... but the differences do seem to be huge thruout.