Boring on the lathe, with a boring bar in the compound slide on a small (not very rigid) machine is never going to be straight-forward. Problems are further increased with increased depth of bore, not diameter. I would never countenance using the compound slide as a means of extending the boring bar.
Mounting the part on the carriage and using a boring bar (supported at the chuck and tailstock) can clearly reduce the number of flexing joints in the process. So far better for deeper (longer) bores, but a pain to set up, of course. I’ve never yet needed to make a boring bar of that form.
Boring on the mill allows shorter cutter extension, so is inherently better than on the lathe – the only real mounting problems being for awkward shaped items. Knee raising is, IMO, better than quill extension when boring (both my mills have knees, but a fair amount of head-space is needed, so I haven’t used the smaller one for boring).
On the lathe I first drill, then bore (if a larger size) – followed by a reamer, if I have one . So much less hassle for most holes.🙂 Much like Howard’s post above.