The sound of digital and cassette are very different.
There is a "roundness" from analog, and a "flatness" from digital, in it's purest sense, but of course the front end mix has a lot to do with the sound. "Signal chain" if you prefer.
A lot of digi-heads are getting analog "warmth" by using analog gear in their signal chain, and/or using plugins that simulate analog.
There is more than one way to skin the recording cat. The Korg CR4 is certainly not it, though, and in the cassette class of devices the 424mkIII is best value in brand new equipment.
The analog - digital discussions will outlive me and my Portastudios, but cassette sound quality is not bad, by any stretch, if you start with high quality tape, a high quality recorder, and use the medium to it's optimum, which takes a little practice.
I've done A/B comparisons of recordings done on an all analog system and digital, within the confines of my own studio, and the analog just sounds better, right out of the box. There's an unholy amount of fiddling and affecting of the sound necessary to get digital to sound as warm and fat as analog. Sorry for the cliches, of course.
I hear one dude after another touting digital, who then goes on to say how great his front end is, which is usually some mid- or top-grade analog preamps, & such. Anyway, a simple in-person A/B comparison pretty much kills any debate, IMO.
A lot of what you hear about the atrocities of cassette sound is from people who've never tried it, and who are just repeating what they've heard. That, or their experience on cassette porta's was with a low-end device, like a Fostex X-something-or-other or Porta-02, and not with the best high end Tascam Portastudios, which are capable of getting fine results, in general.
I won't lie or mislead you on this point: a lot of what your recordings will end up sounding like is due to your technique, not solely based on gear choices,... within reason. Given, is that you'd expect an MF-P01 not to sound as good as a 424mkIII, & a cassette Portastudio not to sound as good as a 1/2" reel tape,... and so-on, up & down the recording food-chain.