Cut and butt.
Sounds like an "Adult" cartoon..
See this joint in wood projects but not in metal - am curious now.
I would say the joint compromises both pieces where but welds on both sides would be stornger. In wood you would be doing it with solid material not hollow. By cutting the box you are weakening it where load is.
I suppose if you are seeking to maximise area of attachment it would have to be mitres.
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