What are the differences between Elder Sign and Elder Sign: Omens?
There is a thread on BGG discussing the changes. They are far to numerous to mention all the changes, but some of the most notable are:


There are no allies.
Spells are cast after rolling, but don't carry over to other investigators.
Only 1-4 investigators instead of 1-8
There are no midnight events.
Assisting investigators aren't penalized when you fail.
Monsters are added automatically, you cannot choose where they are placed.