Your assuming it's one or the other. It doesn't have to be.

Agreed. A loosely aggregated orbital ring of habitats wouldn't require technology much in advance or our own and would increase living space immensely. The next jump to generation ships is also foreseeable. Dyson spheres are revolutionary and progress(?!) is evolutionary. It seems inevitable that the investment would always exceed the return.

Not going to find much elemental oxygen in a gas giant

It's certainly impractical with the technology we have now. However, imagine an alien race that can build very small, self-replicating robots. The first of these robots is designed not only to make a copy of itself, but is also fitted with a solar panel and the means to transfer energy it collects to a receiver, perhaps by means of microwaves or a laser. That robot is then sent out to a solar system where an asteroid belt provides it with the raw materials it needs to make an exact copy of itself.

Imagine each robot can make a copy of itself once in every 24 hours, then start the process again the following day - before too long, you have an enormous number of robots. Once you reach a certain amount, these robots stop building copies of themselves and start traveling closer to the system's star to create a Dyson swarm - which would provide an immense amount of power. Add more robots and you could end up with a complete ring around the star; add more and you can create a net... then, if you still have more raw material, allow the robots to fill in the gaps and you could create a sphere completely enveloping the star and gathering almost all of the energy it puts out - though since a Dyson swarm, ring or net would provide so much power, a sphere probably wouldn't be necessary.

It'd take time. Even if our alien race have a suitable solar system relatively nearby, say ten lightyears away, getting that first robot there would take a long time - if the robot is able to travel at 1% of lightspeed (which is much faster than any spacecraft we've produced so far) it'd take it a thousand years to arrive at its destination. However, once there the process of replication becomes exponentially faster and faster as each new robot is created: in only a few weeks you have a million robots, and that number doubles every day.

It's a big investment time-wise, but the rewards - vast amounts of power - are enormous, and it all begins with one little robot. That seems like less effort than building a fleet of enormous spacecraft to harvest materials from gas giants.

Granted, a Dyson Sphere would be an enormous undertaking and a huge feat of engineering skill. My concern on it: what would the Builders do with all the life on the inside before the star dies?
I personally like Ringworlds (Thx Larry Niven) or Orbitals (Iain Banks' "Culture" novels).