What do we use most by number of parts? probably bolting.
What do we use most by total member weight? welding--our whole frame is welded.
That said, we sort of see their use on 3 dimensions: structural/strong, changeable/serviceable, and weight.
- Very strong, very changeable, weight isn't a major concern: bolt/nut it (with loctite another durable vs changeable dimension).
- Strong, still changeable, weight is a concern: consider steel rivets with backup washers. They're permanent (that how each of our pivot modules is connected to the robot), but if something does go wrong it's easier to change than welding.
- Strong, not changeable, regardless of weight: weld it! This can go for non-structural items too, if you feel like it.
- Less structural, possibly changeable (though not necessarily), weight independent: consider threading and bolting it (no nut) or aluminum rivets (with or without backup washers). Rivets are harder to change, but less likely to change on their own, and a little lighter (not to mention faster) if you're using a whole lot of them. Granted, the threaded hole vs nut trade-off can also come from location issues. i.e. can you fit a nut in there? More importantly, can you fit a wrench in there?
Of course there are exceptions to every rule, but this is usually what comes to mind first.