Standard rechargable 9vs will allow you to run the battery internally for both the B-18s and AD20. 9.6v RC packs will require you to run the batteries externally.
The external RC batteries have a larger capacity and should give you longer run-times than the internal 9vs. Which you run is a matter of personal preference based on [1] whether you want internal or external power, and [2] how much run-time you'd like to get out of a single (set of) battery(ies).
Check the Archival Info forum for a thread titled something like "Calculating Run Time" for how you determine approximate run-time. Then check a thread titled something like "Gear Current Draw" for the AD20's current draw. Finally, calculate your tun-time for the AD20 to determine whether you want to run internal or external based on the run-time they'll each give you.
Sorry, can't help on the current draw of the B18s, but maybe someone else can?