what is the different between reduce bore and full bore and who can select? process scope or piping?
There really is not a process reason to select a reduced-port ball valve over a full-port ball valve.  There is a measurable dP across a reduced port valve, but work done at Southwest Research (for gas measurement, but the concept carries over) showed that with the beta ratio of a reduced port valve virtually none of the (small) dP is "permanent".  That means that if you measure the pressure 10 diameters upstream and 10 diameters downstream of a reduced port ball valve in the same flow you will get essentially the same dP (down to a fraction of a mm of water column) as a full port valve.
Historically, the reason has been cost.  For some reason, prior to about 1990 there was a significant cost savings for reduced-port valves.  That stared to change around 1990, and by 1995 you had to look very closely at your cost estimates--in some sizes the reduced port valve was actually more expensive than the full port valves.  It is still true today.  Even when the reduced port valves are cheaper it is usually a pretty small difference.  On the other hand, it can be really hard to get a pig to scamper through a reduced port valve, and you cannot run a smart pig through a reduced port valve.

If you can say that the cost is a wash, then I can not see any reason why you would ever buy a reduced port ball valve.

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