There is 'deep bass' that comes from actually having considerable ultralow frequency content in the audio, .e.g. some synthesizer music, pipe organ....
But I posit that some (much?) 'deep bass' is just a perception that comes from mixers duplicating bass in the LFE and the mains/surrounds. And then all that bass gets summed into the subwoofer if you use bass management. IMO this is not how it should be. In a rational world, LFE would *only* be used for extraordinary loud/deep bass frequency content...not 'normal' bass. That's it's intended use in movie soundtracks -- LFE = 'low frequency effects'.
From memory I'd cite Steely Dan 'Two Against Nature' DVDA as an example of doubled bass, and the Jeff Beck 'Blow by Blow' (phase corrected) SACD as another. Or any disc that seems to have *vastly* more bass than other discs. If you play music as files instead of discs, it's easy to experience jarring differences in bass content as you quickly switch between 5.1 albums.
(Bass turns out to be a quite complex topic in surround music...as I'm discovering when I objectively compare the same mix released in DVDA, SACD, and DTS/AC3. Actual, measurable, potentially quite audible differences exist in the *bass* of those, and they are not related to lossiness vs lossy. Some day I'll start a thread on this, when I can get back to compiling data. It's potentially a huge thing, yet I've seen no discussion of it.)