Herinaz,
I have never touched an Archimedes, but I have 4 Nucleus. What is the physical in your hands advantages of the Arch over the Nuke?
The Archimedes has it's different primary extraction so the bolt lift only cocks the trigger instead of cocking the trigger and primary extraction.
I think it is an advantage if you are going to reload and push pressures that might cause sticky bolts.
Beside that, it has an integrated recoil lug and a keyed scope mounting rail. Those are features that some people value, some not so much.
Both have a Mauser claw style extractor and both rotate with the bolt (unlike a Mauser or Mausingfield) but since the Archimedes doesn't do primary extraction on bolt lift, in effect it is more like a Mauser claw than the similar extractor on the Nucleus.
The differences are not huge but they are enough to feel a difference.
I think an Archimedes is a good choice for a high performance long action Magnum chambering.
For non Magnum short action chamberings, Nucleus is probably perfectly adequate but Archimedes will do just fine too if you want to spend the money.
Nucleus will do fine with high performance long action Magnum chamberings also, it just won't handle very high to excessive pressure as gracefully.
If you are a reloader who knows when to say when, the Archimedes might help you tiptoe on the edge. If not, the Nucleus might complain more when you are going too far which could be a good thing.