The Omega is a relatively big, mile-munching cruiser. It is not designed to be thrown around B roads at break-neck speeds. When you consider what it was designed for it is easy to understand why it is piss-poor at fast cornering, even in MV6 spec. (I'll get slated for that comment, but the vast majority would probably agree).
The Auto Transmission fitted to the Omega is quite competent and definitely one of the better boxes of it's time. The only thing which annoys me is how (on later ECU updates) the transmission will change up too soon under 'careful' acceleration. I find myself progressively pushing the throttle to compensate which uses even more fuel than it would if it held onto the gears slightly longer (as in the old ECU software versions).
I dont know if you are asking for personal opinion, but if so..... With the Omega and a V6 engine, I'd have the Auto over a Manual because it's just how it was designed and it ticks all the boxes because of that.
Regards.... A person who generally prefers Manual Transmissions.