pih: I wouldn't use builder's fill, it will crack due to expansion over time. Builder's fill sets rock hard and it doesn't tolerate any movement. If you were going to do it I'd do paintable silicone as suggested, and it shouldn't be too hard to make it look ok, but prep and tooling are the keys to a tidy silicone job.

The secret for making smooth silicone joints: squeeze a bead of silicone along the gap ensuring that you neatly and fully contact the two surfaces along the whole length of the gap - don't mind how the surface looks just yet, the seal is the most important, and it's best to overdo it rather than underdo it.

Then, quickly before the silicone skins over, use a spray bottle with lightly soapy water in it and spray the whole thing plus a wiping tool until everything is good and wet (could be a putty knife, spatula, old credit card, or just your finger) and neatly scrape the silicone level with the surface, frequently wiping the excess off on a paper towel and keeping the tool and work surface wet. Allow to dry then paint.

Gotchas:
- practise it first to get a feel for it
- the silicone won't stick to anything that's wet, so you have to ensure that everything you want the silicone to stick to has made contact before spraying
- just do one length at a time and allow to fully dry before doing the next stretch or the silicone won't stick where you might have oversprayed. If you do a long stretch before smoothing it will start curing and it's game over.
- not all silicones are paintable
- no silicone based fillers are sandable, so prep your wood before you silicone
Ensure the surface the silicone is adhering to is completely clean from oil (including fingerprints) and completely dry. Ideally wipe well with meths or IPA and allow to dry
- be wary of silicone-like polymer/co-polymer fillers like Selley's All Clear: these set quickly and the smoothing method I've shown above doesn't really work.

@pih What about that exposed raw gib edge? How would you deal with that?