QGD or NID/QID against 1. d4?

Which one is more drawish?

If black doesn't want to lose (win or draw result needed in a competition), which one should he/she pick?

whichever youre more comortable playing

If you have to ask, the answer's are probably going to be irrelevant. What makes you think that one opening is going to make YOU immune to defeat? Try putting on your thinking cap and deciding which opening(s) suit your style and preferences. Offhand I'd say you should concentrate on double QP openings before tackling single QP openings.

I'm just asking which one would be safer/defensive, 1. QGD or 2. NID/QID?

Obviously, the Petrov would be safer than the Sicilian.

Usually, the lines of the QID are considered to be drawish.  The lines of the QGD are usually considered boring/passive as Black, holding until the endgame.  The NID is very sound, and gives many chances for imbalancing the position.

if youre absoloutely at equal comfort and skill in both I'd recommend QGD.
It creates much less imbalance in the position than the nimzo and you can get by on considerably less theory imo. Look at the lasker (id recommend) and tartakower variations.

Yes, familiar with both, but I would like to concentrate on only one, either QGD or NID/QID. The one which is the more safer/defensive. Which one do you think will least likely lose?

I don't care whether there is a lot of theory. I just want to pick the safer/defensive/drawish opening. An opening where you'll most likely not lose (draw result or don't care if it's a win).

Why do you have such a negative mindset?

I'm a fan of Karpov, Kramnik/Drawnik, Petrosian, Leko and Ulf Andersson. Taking no risks but reacting if my opponent makes an error.

"Don't force openings, wait for them."

Go for the QGD, much less imbalance, therefor more drawish (due to less sharp lines).
In the lasker variation pieces are traded off quite quickly and can result in a pretty fast endgame with little weakness for black. 

In all honesty, both openings are considered the most sound responses to 1. d4.

I think everyone should have the QGD in their repretiore, once you have masterted it, then you can proceed to learn other defemses.  A great reportiore for Black would consist of the QGD, Nimzo-Indian, and the Ben-oni.  Starting out 1...Nf6, 2...e6 keeps all three options open.  

This fear of drawish chess is only something that players +2400 should worry about. For example, the Russian (Petroff) Defense has a draw rate around 27% for players rated U2000, and the Sicilian has a draw rate around 24% for players in the same rating range. Even the French Exchange variation give less than 1 in three chance of a draw!

Don't worry about which opening is more drawish. Worry about understanding the opening and learn what the key ideas are. As long as the opening is sound, the better player will win the clear majority of games.