If I recall correctly, the specs on Verizon's website says that the Omnia does not support e-mail. This was the deciding factor on getting the storm, for me.
Here are some facts.
The Omnia
http://www.verizonwireless.com/b2c/store/controller
The Storm
http://www.verizonwireless.com/b2c/store/controller?item=phoneFirst&action=viewPhoneDetail&selectedPhoneId=4286&lid=//global//phones+and+accessories//blackberry+devices//blackberry+storm
(BlackBerry Internet Solution (BIS) – integrate up to 10 personal email accounts)
This was not found on the Omnia, so if E-mail is a big factor for you, I would think twice. If not, then buy the sweet pocket PC.