Yes, choosing the proper drive(s) for TRT testing is important.
There are many types of trouble a disc can have however, so one drive may be fussy about some types of probles while another drive is fussy about other types of problems.
My NEC, Optiarc and Pioneer drives are fussy in general about bad burns, the same is true for my Plextor PX-712 but that might be because it's far more fussy than other drives of the same model. The same discs can be TRT scanned in my BenQ and LiteOn drives with flawless results.
My LiteOn drives and especially my BenQ DW1655 drives are fussy about certain re-linking points created by NEC 4551, Optiarc 7173 (now dead) and Matshita 840 drives. The BenQ 1655 is completely unable to read some sectors while the LiteOn drives merely have problems reading those sectors and slow down or fail during a TRT. The same discs have flawless TRTs in my other drives.
So my point is that even though you have found a drive that is fussy about some problems, don't expect it to be able to detect all kinds of problems.