I have never played an omen, but the stileto delux is what really sold me on schecter basses. I was so satisfied playing that thing in the shop that I felt comfortable ordering the stilleto custom 6 with out trying one first.

from what I can tell the stiletto has mahogany with a maple veneer where the omen has basswood.
the stilleto has a 6 bolt where the omen's description in the schecter guide only says "bolt neck"

other than that they are identical from what I can tell.
no sir away a papaya war is on
I am judging this on the six string versions, but the principal is the same really.
'Nuff said.

But I'll say more anyway.
The Omen did not feel good. It felt cheap and awkward to play, the stiletto, on the other hand, played like a dream and sounded great. I never heard the Omen, because I didn't play it through an amp, but the Stiletto sounded cool. I ended up buying the Stiletto Extreme Custom which is better, but still the Deluxe was nice.

Ibanez K5
Warwick Rockbass Vampyre 4

Line 6 Bass Pod XT Live
Epiphone Les Paul Custom
i think they will sound similar. they have the same pickups, pre-amp, bridge, and neck wood. the only realt difference in tone will be the mildly different body shape and the basswood vs mahogany.
no sir away a papaya war is on