I tend to gripfill the gaps on all architrave and then paint over it when painting the doorframe.
If you've already painted and just want to neaten it up, I'd probably caulk it. I've used exterior acrylic caulk to good effect when worried about any moisture. Silicone generally is a ballache later down the line because a) dust absolutely loves sticking to it and b) you can't paint over it when you re-decorate.
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