Obsolete? Not really. Use the original if you and your players want. Not like there's an official tournament scene or the Game Police are going to kick down your door.
There are minor changes to the core rules in the Omnibus. Default Movement is changed from 4" to 6", for example. It rolls in material from the TSTE + SGDAF Augs. There are a couple new weapon options for Agents. Fewer Macros. New options for H-SEC and including shadowrun-esque fantasy tropes.
As to which to purchase, I'd suggest the Omnibus. It's complete in itself with all the pertinent material compiled and clarified. Get that and you're good to go.