Length and weight are the only real differences.
The ropes aren't as strong, but stretch long distances and are lighter.
When to use them is personal preference and whether either works
for what you need. There's no formula. Trial and error until the learning curve is done.
Does that answer your question?

I would add that the overall sturdiness of your construction will become a factor - the elastic tends to "bounce" a lot while the beams are more rigid.

What's with the "price" difference? Does it make sense to save money?

Originally posted by Nice to Have:

What's with the "price" difference? Does it make sense to save money?

^^Bump^^

Other than reducing cost of the overall construction. So unless you have OCD and want to reduce wasteful spending there’s no benefit to it

Rope has a number of huge advantages ie that it's light (so your structure won't collapse), long (so you can support from a massive distance above), quick and very versatile to build with, and of course cost. Its big disadvantage is that it has no compressive strength (so you can't use it to support a road from below for example). And of course you can't drive on it.

Rope opens up a whole new bunch of options for easy construction, eg you easily suspend a small platform on an angle in precisely the right place to deflect a dropping cube.

It is really useful for redirecting forces, eg preventing a structure from twisting sideways or dropping down, when combined with a suitable pivot point (eg a rope running from an anchor on the left, to a structure point on the right, then continuing the rope down to support a structure).

And because it is so light, it is your first "goto" for deloading force when your structures are red or collapsing (because adding more beams can often make your problem worse by adding more weight).