I have a 2011 Squier VM Jag Special, and a 2011 Squier VM Mustang. Two totally different animals. No pun intended.
The Mustang is my go-to bass, and has been for a while now. The short scale string tension took a bit of getting used to, but I don't even notice it now. It has the original "Duncan Designed" pickups in it, and to my ears, it sounds like a Mustang should. Warm and wooly. The neck is fine, it works and all that, but it's not what I would call fast. Mine feels a little chunky, but not in a bad way. The short scale makes for a much reduced reach, which is something I really like.
Of course, string selection is a bit of a hassle with the bridge. LaBella makes a good selection of strings particularly for this bass. Mine is currently strung up with some medium scale D'Addarios and sounds great. The offset body isn't that much physically smaller than the Jaguar, but it feels tiny in comparison. My main complaint with the Mustang is the lack of a forearm contour. Slab body for the vintage vibes, I get it, but it's sometimes uncomfortable if I'm playing sitting down for a long while.
The Jag is a P/J, so I can't comment on how that sounds compares to your CIJ. The P pickup solo with the tone rolled off sounds quite a bit like the Mustang. After playing the Stang for the past few years, the standard scale Jag feels big, like I'm wearing a sweatshirt two sizes too large. It is, however, pretty darn comfy, and once I've re-adjusted to the 34" scale, it feels good.
If I were to buy another Mustang, I would definitely consider the Fender Player II. Non-string through bridge, P/J pickups, lots of nice bottom end. I've had hands on these a few times and I really like them. Or, if you're going for the vintage vibe with standard Mustang pickups, the Vintera II is a sweet little bass.