Digital vs Analog output on CD players

Folks, I'm sure this has been discussed before but I can not find the thread. I'm in the throws of experimenting with connecting my two CD players (yes I use two for the fun of the hobby and switch around; some CD's sound better on the NAD and others on the Rotel) via their digital ouputs to the digital inputs on my A-V receiver vs their analog jacks. What's the official scoop on this? Does using the digital outputs improve the overall soundstage, depth, detail, etc of the music being played? Are there any other benefits going digital vs analog? My hi-fi store sold me a digital interconnect and is letting me try it out. I can always go back to analog. I have the my NAD C541 connected via its digital output and my Rotel RCD-1072 via its analog outputs. So far, I am finding the differences to be subtle. What does everyone think on this? Many thanks. Sorry if I sound naive on this topic.
I would only use the digital out on a CD player if you have a better external DA to use. A high end (newer) CD player should do a better job then a mid-fi receiver. But for awhile I was using an old Sony CD player (surprised it had a digital out) as just a transport into my B&K processor since it was much newer. DA's keep getting better and cheaper every year. Now I have a great CD player, SACD player, and preamp so I only use the analog outputs.