To answer that question might take just two minutes* of manipulating them, and likely taking some parts off, partial disassembly — taking them apart just enough to see what's different or wrong. Not something we can do over the internet though.
Here's my best guess though: There are two holes in the cage to take the tail end of the rotation spring. There are also two holes in the spring cover that contains the rotation-stop screw. The tail of the spring should go through the
same holes in the spring cap and in the cage. Like if the spring goes through the left hole in the spring cover, then use the left hole in the cage also.
The mech with the unusual (probably incorrect) angle is the older one. You know how to tell which one is older right? We can explain, if not. Anyway on that one, if it's still at a wonky angle after the previous step, try fitting the cage onto the "other" hole, whichever one it's
not in now. Just spitballin' here.
Do you know you need to preload the cage-rotation spring, before you put the rotation stop screw back in? There's no way for us to tell from a photo if that has been done.
With that stop screw out, you rotate the bottom of the cage forward like feeding out chain, this makes the spring push back the other way. After you've preloaded it enough that the rotation stop screw location becomes available, put the screw in. Now the cage wants to rotate back the opposite way from your preload, so the stop screw is pressed firmly against the bottom parallelogram "knuckle".
BTW, your older mech has the original top knuckle that is not reinforced below the upper pivot, so it's more prone to breaking there, like if the bike falls over or you shift into the spokes. Treat that one with extra care if you put it on a bike. Unfortunately the reinforced ones, like your newer one, break there a lot too. It's not until you get into really late Rally models (that looked completely different) that you get one with a properly designed upper knuckle. And made of aluminum like God intended, not that weak
and heavy Zamak of the first couple generations, a notoriously bad decision on Campy's part.
Going even further from the question you asked:
I see the chrome on one or two of your pivot bolt heads is a bit scratched/rusty. Evapo-rust followed by polishing will make them look a lot better (if you care), but not like new, and replacements are pretty much nonexistent. Another option,
if you're fancy, is titanium replacement bolts from Jim Merz (if he still has any). I got some 'cuz yeah I'm fancy, and they're beautiful.
