Sahe_Bassist, even though my VM and my CV are heavily modded, I can offer this...
The pickups are different. The Duncan Designed pickups on the VM series are really very good pickups. The CV has great pickups too, but I prefer the Duncans myself. Can't really say why. I have played VM and CV basses side by side, through the same amp, several times. I always came up liking the tone on both of them.
The finish on the necks is different as stated before, but the neck profiles are also different. I much prefer the feel of the VM neck over the CV. I sold the CV neck and replaced it with a 70's Classic bound and blocked Fender neck.
The CV bodies are basswood and the VM was soft Maple. The newer VM basses I believe are also Basswood. Check the specs on the Squier site...
The VM uses the traditional Fender style bridge and the CV has a really nice, high mass bridge with brass saddles. I changed the bridge on my VM to a Wilkinson Fender Style bridge with brass saddles. Why? I like the look and like brass saddles, for no other reason than I like them. Kinda throws a vintage vibe when you look at them.
The VM (again double check for the whole line) jazz has cavities shielded with graphite shielding paint. I am unsure about the CV as mine is shielded with copper and was that way when I got the bass.
Bottom line is they are all great basses. I suggest you get to a big or good local shop and try them out. Decide for yourself which one has to follow you home....
I believe the Classic Vibes are amazing quality for the cash. In some weird subjective way I feel that the maple fretboard ones have the best fretwork.
I think they are amazing basses, despite their low cost! I wish we had such nice basses when I first started out!