A colour CRT display, whether a television or computer monitor, in the end always sends separate R, G and B channels to the picture tube as well as using a sync signal to control the scan. With a source that originates RGB, the quality differences depend on what other conversions the source applies that the display must undo in order to generate the RGB signal for the picture tube.
By far the largest improvement in colour display quality was gained by using RGB instead of a composite colour signal between the source and display. The difference is huge and easily visible if you compare the RGB and CVBS outputs from the same system on a monitor with both RGB and CVBS inputs.
RGB sends three separate analogue¹ luminance signals over three wires. The sync might also have its own one (composite) or two (separate horizontal and vertical) wires or be overlaid on the green signal; this makes no visible difference because the sync is very easy to separate and occurred only in non-display areas (off the edges of the screen) anyway.
Using a CVBS colour signal² caused a huge reduction in quality because the colour information was transformed drastically (to NTSC colour or PAL colour) in order to be able to use a single channel; this was also destructive to the colour information because they had to reduce the overall bandwidth of the signal. (Essentially, the resolution of individual colours is lower than the overall resolution of luminance ("brightness") information.)
(As mentioned in a comment below, there is also a similar form of signal, often called S-video, that uses the same luma and chroma signals but transfers them over two separate wires, rather than mixing the luma and chroma into a single signal down one wire. This increases the resolution of the luma signal back to its original monochrome resolution—luma resolution is otherwise reduced because the chroma signal is using up some of its bandwidth—but the colour resolution remains poor. This produces a small improvement in image quality, but it's nowhere near the improvement you see with separate R, G and B signals.)
A monochrome CVBS signal, on the other hand, contains only luminance information for a single channel, and so is electronically exactly the same as a single channel of the RGB connection with sync, such as the sync-on-green situation I described above. So with a monitor, so long as it is not trying to filter out parts of the signal that would be used for colour in a CVBS colour system, will display a monochrome signal just clearly as an RGB colour signal. In fact, you can plug a monochrome CVBS signal into the green channel input of an RGB monitor and it will display just fine. (This assumes that the monitor supports sync-on-green; if not, sending the monochrome CVBS signal to any or all of the RGB input channels and the composite sync input will usually work.)
The transformation from a baseband CVBS signal to that signal modulated onto another signal in the a radio frequency (RF) range will, and its reversal at the display end, can be the source of a slight degradation in quality, but except in pathological circumstances this is nowhere near the level of degradation introduced by RGB/CVBS/RGB conversion. In good circumstances it will be barely noticeable. In less-than-great circumstances you might see more degradation of a CVBS colour signal than of a monochrome signal, which is rather the opposite of what you're thinking of.
The signal quality differences I'm describing above ones that I've seen and A/B tested myself on various computers that produce both RGB and monochrome CVBS (e.g., the Fujitu FM-7), RGB and colour CVBS (e.g., the National/Panasonic JR-200), and CVBS and separate chroma/luma (e.g., the Commodore 64). The tests were done on a professional video monitor with inputs for all of the above, a Sony PVM-9045Q. This is a late-'90s PVM which cost about $2000 when first introduced and has very high quality analogue decoding circuitry for CVBS/NTSC/PAL/etc.
¹ Digital RGB signals were also frequently used, but from the picture quality point of view these were essentially the same as analogue signals; the only thing that changed was that the monitor would do a trivial 1-bit digital to analog conversion. Essentially, this just converted a 0-1.8 V digital input to 0 V analogue, and 2.4-5.2 V digital signal input to ~1.0 V analogue.)
² This was also sometimes called a "composite colour" signal; I avoid using the word "composite" here because it may refer to combining all three colour signals together into a single signal or, even in a monochrome system, combining luminance information with sync into a single signal.