I thought about it long and hard and I really dont think there is a major difference between the meaning of the two.

After 'with' the -ing form is called a gerund and describes an activity. In other words the verb has the character of a noun.' I'm not comfortable with speaking in public' .Without 'with' the -ing form can either be a) a gerund as it's not necessary to use 'with' ' I'm not comfortable speaking in public' or b) a present participle describing an incomplete action.' 'I am comfortable sitting here'