Running with teams is a good way to get drops faster as you can traverse the dungeons faster. I found it is all random but it is true running lower level dungeons solo will give you a bit more as you will obtain all the drops. There is no magic startegy to get rare vanity or pinks as these are very random. Keep in mind drops are now scaled to your level now so most drops will be equal to your level except vanity drops (which is very rare I have been playing for over 2 and half months and still have not seen a vanity drop).

Just be sure to open all chests along the way as this will also give you gold on all opens and an occasional red and or blue stimpack with the drop.