Is it worth upgrading a CD player?

I don't think it would be much improvement unless you spent $$$ on a dedicated player without a dac inline (black ice audio cdp, marantz sacd/cdp, etc)

Actually there is considerable difference between a CD transport (what you are using your Marantz as) and dedicated transports. I have and use regularly an Audiolab 6000. A transport on devise. I have 3 very good CDP’s - used as a transport alone the Audiolab is ’better’ than any of them, however when used as a CDP they sound much better. If you are happy with your present DAC I would simply upgrade your ’transport’ to something like the Audiolab. Cambridge has a pretty good one as well. Personally I would investigate getting a good DAC and Transport.

To answer your basic question about the level of improvement I would say this depends on your level of listening skills and the importance to you of the differences you might hear in new stuff. If you are presently happy with what you have, why change, just continue to enjoy your music.

Big difference as @newbee stated. Look for a slightly used Bel Canto CD3t, compact, and built like a tank. I have one and love it. Love the small footprint and big sound even though most my CD's are now on my Innuos Statement. 

@newbee

+1

Transport. But,

Also, it will depend on your other equipment. Rega makes a really large range integrated amps from extremely inexpensive to much less inexpensive. Which do you have and speakers? What is your longer termed goals? Move your system up? Or just bring your CD player closer to your vinyl playback?

If thinking longer termed, I would consider a streamer as transport instead of physical media. For the price of a CD / month you get access to a nearly infinite amount of music, much at a higher resolution than CD. Streaming can equal or exceed the sound quality of Other digital content or even vinyl at different price points.