Learn English – Is it appropriate to omit “to” after “ought”

Semantically, there is no real difference between the two constructions, and they can be used interchangeably. I agree with you that "should" has become the far more common construction.

Even back to the Old English (and earlier Proto-Germanic), the words carry a nearly identical sense of obligation. As such, I'd be hard pressed to articulate even a minor connotative difference between the two forms in modern usage.

I agree with Peter Shor's answer, however, looking at this phrase in the COCA corpus, there seems to be an exception that is most prevalent in spoken English where ought not be is a frequent although still less common alternative to ought not to be. For example:

...one could argue then that President Bush ought not be succeeding.

2005 Tavis Smiley, PBS

Searching a selection of classic texts I found no instances of ought not be, and British English also appears to reject omission of the 'to' in negative ought. So I would tentatively conclude that this is a development in contemporary American English.