"In your configuration, if both LTO3 and LTO4 tapes are available and an LTO4 tape drive is being used to backup, will the default behavior be to select an LTO4 tape? Or is it a random chance that either could be selected?"
you have to look at drive type and media type
( issue is there is no Hcart4 in the software)
if your LTO3 drive is set up as hcart3...
and your LTO3 tapes go in as hcart3
it will only pull hcart3 tapes for hcart3 drives.
for my LTO4 drives i set the up as hcart
i then have my LTO4 tapes go in as hcart
it will only pull hcart tapes for hcart drives.
so look at your device monitor and see what Drive type you have set.
then go to your media and see what they come in as. if not correct you need to set up Barcode rules.