those will sell in very good condition for $1200-1700 from private sellers. Dealers often more like 2K+
this one is not in particularly good condition. the gold bar Connies have more value, as the gold is actually gold. But this has value itself. I wouldn't throw it away. You might not get but $400-800 for it. More towards the lower side to someone who will use it as a parts watch. Movements can go for 200 or so. the gold bezel for 150, etc....
I don't know if you particularly like the watch, (it looks like it was well worn), or if it has any sentimental value. Omega offers service and restoration. It comes at a cost, but it is less than the cost of a new Constellation. You can take it to an Omega dealer for a better idea on cost.
Many vintage watches hold more value to a collector in an as-close-to-original shape as possible. This one looks well used to me. For a "dress" watch such as this, I'd just as well have it look like one. I'd consider the service with a bezel touch up and lightly polish the bracelet and have it looking like new. (Again, collectors would tell you "NO!", but I like to wear a watch, not just let it sit.)
Sometimes, you can get a local watch guy to service it for less than Omega charges, that is a way to go if you don't want to pay the Omega premium. Omega will replace original parts if they deem it necessary, locals will often try to salvage as much original as they can.