Hi Tim,
I've had both phones so let me outline the main advantages and disadvantages of each phone

!!
Samsung Omnia
Optical Mouse (the xperia only has the option for you to use it as an up/down control, but with the Omnia you can use it exactly as a Windows Mouse!!)
Samsung Today Screens & Samsung Adaptation to Windows -
Basically Samsung have put quite a bit of software on the phone so that you don't have to use the DEFAULT windows mobile options as such - in a nutshell, it's more finger touch friendly!!
Internal Memory - Depending on your usage, a lot of people will find having an internal memory very useful - it's available with either 8gb or 16gb of memory so if you're a media user then you might prefer the internal memory and MicroSD card compatibility of the Omnia to the 2GB/4GB included memory card of the Xperia.
Sony Ericsson Xperia X1
Metal Finish Body - Personally, I prefer the metal body of the Xperia to the plastic feel of the Omnia!! Also I have had TomTom on both, and the Internal GPS of the xperia is much better than that of the Omnia as firstly TomTom picks up the internal gps receiver on the xperia but requires you to configure port settings and install other software on the omnia, and it picks up satellites MUCH quicker on the xperia than on the Omnia!!
Full QWERTY Slide Out Keyboard - In my opinion, if you get a touchscreen phone you have to be prepared to actually use the touchscreen, but sometimes its very useful to have a full keyboard to use specially when you're using creating and editing documents!!
Stylus - Obviously, both phones come with stylus, however the Xperia has an inbuilt stylus slot so it looks more sleek than the Omnia which requires you to attach the stylus to the phone at the top on the side so it hangs loose and looks ugly in my opinion!!
Overall, my preference has to be the Xperia as I'm not that much of a media user but prefer the slide out keyboard and inbuilt stylus slot to the extra memory!
That's pretty much all I can think of lol but if you want to compare the phones to others or want more specs, check out my battle of touchscreens post (follow link in my sig) and check out
GSMArena.com - GSM phone reviews, news, opinions, votes, manuals and more... and search for each phone!!
Hope this has helped you,
Nirave