OK. You have been given contradictory advice because there is no clear answer for this one. No one has all the experience in every area and no one has a crystal ball. But here is my tuppence worth.
Firstly, I think I depends very much on which area of the world you will be working. Some areas are well developed with lots of infrastructure (e.g North Sea) other areas are not (e.g Arctic). Secondly, think about the water depth of the developments completed there. North Sea is shallow (typically up to 200m), but offshore Norway ranges from shallow to deep (up to and beyond 1000m).
I work mostly in the North Sea which is a 'mature' basin so the fixed infrastructure is in place. All the structures I work on are 'Bottom Fixed', mostly the production is either tied back or goes to a new FPSO.
My first thought was whether you are thinking specifically about platforms or all the types of structures. Fixed platforms are still being built but certainly not as many as there once was. And they are restricted to shallow water. Floating platforms (FPSO's, semi subs etc) are more common in the North Sea because most of fixed platforms are in place already. New ones do go in occasionally however.
Bottom Fixed Structures to me doesn't just include Fixed Platforms, but also Subsea Manifolds, Templates, Protection Structures and all manner of smaller structures used for subsea field tie ins. Lots of new field developments are small and cannot justify the capital expense of a new production facility, in these cases the fields are tied back to an existing installation. So for this the structures are generally subsea. Also as water depth increases the structures are generally subsea, and then tied back.
Floating Structures have a large element of Naval Architecture involved in their design, which is a degree on its own. I have never been involved in the design of any floating structure. The projects I have worked on which have included them then they are typically designed by the shipyard that builds them. Things like FPSO's are basically vessels. Mainly designed by a Naval Architect or similar disciplines.
In general we are definitely moving to deeper water depths as the technology improves. Once we get to seriously deep water the challenges of both types of structure get interesting.
So there is not a 'correct' answer for you. I would suggest you look at the type of infrastructure where you intend to work and the type of projects executed there. Then, using your crystal ball, try and decide how that area will develop.
My first degree is in Civil Engineering. I have found that it is perfectly applicable for on bottom structures. When I have done small modifications to vessels I start to move into the field of Naval Architecture. Over the years I have learned enough to get by with small stuff but wouldn't know where to start on a whole vessel. Not my discipline.
Another aspect to consider is decommissioning. In the North Sea we are starting to look a projects to decommission fixed structures which are at the end of field life. Over the coming years as the reserves begin to run out there will be more decommissioning projects coming through.
Just my thoughts.