when moving one player, i always try to move players to the same position they were in on the previous table - in relation to the button. for example if i have to fill a seat on one table that's at the cutoff, i'll pull someone from the cutoff on the other table. drawing cards is what i do when i move an entire table.
At my home game we always move the last person to have dealt from the larger table and then we place them at the cutoff at the new table. Regardless of where the busted player was sitting. So, as soon as table 1 loses a player, we stop play at that table and wait for table 2 to finish their current hand. Then the person at table 2 that just finished dealing moves.