The difference between a 360 turn, (or two consecutive 180’s or four consecutive 90’s), and a hold of course is that with a hold you get an outbound one minute straight leg to adjust your tracking (3 x inbound drift) to allow for crosswind, placing you in the right position to roll out correctly on the inbound track. This will help you make sure you are where you think you are.
A manual 360 rate one turn does not give you this opportunity for tracking compensation, so the risk is that you might drift over to the non-holding side?
Having said that, if you press ‘Immediate exit’ on the FMGC having just flown over the fix, the Airbus FBW FCOM says it will exit the hold when next overflying the fix, and the diagram shows what looks like a 360 turn. So presumably it compensates for wind drift when doing this - by adjusting bank angle? If flying a 360 using heading mode, I guess this compensation would not occur?
I have flown this approach into Bodrum quite a few times and you had to watch very carefully where ATC vectored you.