The only differences I have heard between CD and DVD-A (I find something irritating in the sound of SACD...perhaps it's the weird phase issue I have read that it has) is between
original analog masters that have been recorded to both CD and DVD-A discs.
One listen to
Neil Young's 'Harvest' on a very modest player tells you all you need to know...DVD-A is better...at least when the original recording is captured in full analog essence. The CD is lethargic sounding and the DVD-A recording is soulful, extended, and energetically captures the nuances in the landmark recording.
Most of the music the last 25 years (starting with Ry Cooder's disc in 1979 or so if memory from my college radio station days suits me) has been recorded at 16/44.1.
Nothing you can do on the playback side will improve upon the shortfall of 44,100 samples per second and other issues associated with the technology now some 30 years old.
Some don't mind it - and some have invested in great DAC's, players and hard drives to mostly overcome - but it's got it's share of issues. I think the real major one is that 44,100 samples per second isn't enough to capture the essence of the original recording...most often noted in the midrange thru (most notably) treble range.
Same thing with vinyl. If you listen to music originally recorded at 16/44.1, then adapted to vinyl, it's generally bad. No matter what you do on the playback side, analog or not, you cannot overcome the original errors of a 30 year old technology.
If you hear an original analog master or purpose recorded 24/192 recording on even a cheap DVD-A machine(Pioneer, OPPO, etc)......you'll realize there are indeed differences of fairly large magnitude between the formats...but only if they weren't recorded 16/44.1 in the first place. Put a Dakiom stabilizer on your player and you'll be enjoying CD or DVD-A every time...add tubes to your system somewhere to gloss over the digital gaps and it'll be really quite pleasant to listen to
Whether it's worth investing in DVD-A discs and a player without any music from the last 25 years deriving beneift from it is an individual decision...one which I'm not so sure of either way