If you can ride at any time at home (no roommates or you have an isolated room/area, no shared walls/floors/ceiling with neighbors) then I'd get the trainer. With a trainer you need a massively powerful fan. I also watch vids and listen to music if I can.

For a busy household that needs to be quiet it might be easier to get out and ride, but there's a substantial amount of time spent getting ready and getting back to normal. Figure 20+ minutes to head out, 10 minutes coming back in. Plus if you have any problems, like a flat, it's a real pain.

Training outside does use more energy by far, if that's a concern.

Training outside will also teach you riding skills, if you allow yourself to learn.

If I ride outside in the winter my inclination is to ride my mtb, a traded bike that's pretty beat up. However I almost always ride indoors.