Use the leftovers. In the end you'll heal more hp with thengiga drain plus big root but leftovers means you dont have to use giga drain every turn allowing you to use a stronger move. So by using giga drain you don't do as much damage and take a hit or you could ko and not take a hit. Leftovers is the better choice. The restored hp varies on damage, you would gain 65% of the damage.
If the holder uses a draining move (Absorb, Drain Punch, Dream Eater, Giga Drain, Leech Life, or Mega Drain), the HP gained is increased by 30%. The HP gained from Ingrain and Aqua Ring is also boosted by 30%, bringing them to 8.125% max HP healing per turn. Leech Seed heals 30% more, but doesn't inflict more damage on the target. It does not increase the health gained from Heal Order, Milk Drink, Recover, Roost, Slack Off, Softboiled, or Wish.
Big Root's effect is highly situational, leaving it as a gimmick at best. Increasing the HP recovered through draining moves sounds good in theory, but the strategy needed to pull off such a strategy is highly inefficient and outclassed. Moves that are affected by Big Root, like Giga Drain and Drain Punch, typically don't have high Base Power, leaving them outclassed by their more powerful attacks. Big Root is basically a knock-off of the item Leftovers, except it doesn't restore HP every turn and is dependent on how much damage your Pokemon can do to the opponent's Pokémon. Unless you plan on running a set containing Ingrain, Leech Seed, and Giga Drain (which is not recommended), Leftovers is the superior option.
Credit to smogon for the second paragraph.