OK firstly we need to clarify... civil engineering or structural? The stuff you've been talking about so far is structural rather than civil. Civil deals with things like roads and bridges - in fact bridges are one of the few things where engineers get to be creative without much input from architects, as unlike buildings their function is entirely to take a load.
Generally it's going to work something like...
1. Architect draws pretty picture of a building including floor layouts etc and comes up with something the client is happy with.
2. Structural engineer looks at architect's plans and proposes ways to hold up the floors as well as make sure the building is stable in high winds etc.
3. Between client, architect and structural engineer they agree locations of things like columns, load-bearing walls and building cores, floor thicknesses, how it will be braced against wind and earthquake loads etc. The client wants to maximise floor space, the architect wants it to look pretty and the engineer wants it to stand up and be stable.
4. Architect goes away and does detail designs of all the decorative features of the building. Structural engineer does detailed analysis of all the structural elements and thinks about things like fire resistance, exposure, floor vibrations, frame stability, seismic modelling and so on. They select the right structural members etc. This is where they get out the relevant building codes and make sure all the structural bits satisfy them. Even if they follow the codes it is still their fault if something goes wrong so they have to be extra sure and often hire other engineers to check their designs.
5. At the same time the other engineers (building services etc) will be deciding how stuff works and agreeing it with the client and architect.
6. As the thing gets built the architect often visits to make sure things are going properly. The structural engineer often visits site during the structural stage, which is often the first and biggest bit of construction, to make sure the frame (normally concrete or steel) is being put up correctly and also to decide how to deal with the cock-ups the contractors will inevitably make. An important thing is that once the structural elements are completed the structural engineer doesn't have much to do but the architect is fully involved right up to completion.
Both architects and engineers prepare lots and lots of drawings... importantly it's generally not the architects and engineers who do it themselves, instead they employ CAD technicians (draughtspeople) to do it for them.
To be honest they are very very different jobs and if you're struggling to choose you obviously don't know the differences between them. I considered architecture once but went for engineering as I'm good at maths and the physics appeals to me. Architecture is very much like an art course and engineering is very much like a science course. And architects and engineers who achieve a lot can both earn a fair amount as both have a lot of responsibility - unfortunately it's generally architects who get all the recognition!