Either will do nicely. The range you specified is fine for both rounds. If I was expecting to do the majority of my work on the near end of that 0-130 range (treestand in the woods), I would be choosing the 30-30. At the far end (overlooking an open field), I would be picking the 6mm.
I currently shoot the 30-30, handloaded with Winchester PP 150 grain. I have not had any shots out past 70 yards with this bullet, but the damage I have seen rivals my other .308 rifles at similar distances.
In factory ammunition, most of my in-the-know friends recommend the 170 grain Remington Hollow Point. I did some quick peeking at the Remington site just now; it confirmed what I was thinking: 30-30 is generally a 150 yard round; the 6mm is better out beyond that.
As to the Lever-Whats-its, all I can say is that some folks have had wonderful results and some not so wonderful. Either your rifle will group them well or not. If it does, you may be able to extend your range considerably with your 30-30. However, you've said your operating range does not exceed 130 yards. In this case, the standard 150 grain and 170 grain factory loads are just fine. A rifle that does more at 300 yards usually does not have additional benefit at 30 yards.
Marginal shots? Neither one of these rounds is magic. The best thing I can tell you is don't take marginal shots. Neither of these rifles will improve a bad situation. I am a big proponent of double-lunging the critter and hoping to take off the top of the heart in the process. Neither round can be counted on to do that by way of the tail.