Can you give details of the two approaches you mention? I'd be interested to take a look.
If the beacon in use is the same for both the L/DME and NDB/DME approaches, perhaps the use of one track rather than another allows lower minima to be used (ie better obstacle clearance), but the other is aligned with the Runway QFU (as could be the case when the beacon is specified as an 'L' or 'OM' for another approach).
I can't see any operational implications of using one rather than the other though; if the weather is cr@p pick the one with the lowest minima, if it's nice pick the one with the minimum runway/FAT offset. Or as cleared by ATC, natch.