Everything's been said already, really, as its credentials and reputation are so well known. I can only provide my perspective on owning it.
I love it, and I'll likely never sell mine (it's the ship in the profile pic, btw, as that's from a screenshot. can't for the life of me remember what planet that is, though... ). I plan on landing in the Sol system when Horizons arrives, just for sentiment. I don't really use it anymore, as the Type 6 is a much better trader, and the Viper IV is a better warrior of a ship in a fight. But the Cobra flies better and has more charm than either.
However, despite the 'each to their own' caveat, I don't see any purpose in buying more than one. You'd get bored of the cockpit, for one... ;-) ED's range of ships can be--- er, idiosyncratic and rather semi-broken at times (see below re the DBX), but there's still a range of vessels suited for certain roles, so it only makes sense to try them out.
I kept 8T cargo for small runs, or even a few rares if a station's nearby, but mostly kitted it out to be a bit of a lite-explorer/science vessel; both of the top tier scanning modules, a decent fuel scoop, and an AFM. Never needed the AFM, but it was only a first trip outside the bubble to the Pleiades, so it wasn't anything too risky at all. I kept the shield and weapons, as I wanted that trip to really pay off - so ensuring I stayed alive was kinda important. Made my first millions in that ship.
The Cobra III is sufficient for some roles like missions, exploring and rares trading, and is underpriced. Its primary attribute is being able to boost away from just about any threat. But eventually you will want more cargo capacity or jump range or agility or something. I keep one in a home port for running low-cargo missions, but prefer the AspX as a generalist now that I can afford it.
The AspX is a demonstrably superior ship to a lot of things, and I should be saving for it for Horizons. However... I think it's ugly as sin, and if I get it, I simply won't ever fly the worse ships that I love the look of (Diamondback Sucks-At-Exploring-Post-Horizons Explorer says hello). Simple affection for the look and feel of a ship is an easy thing to forget, but if players prioritise stats over anything else, surely a lot of fun is being missed.