The LD 50 listed on the wikipedia page you link to is 90 mL/kg, which would be about 6 liters for a 68 kg (150 lb) person. This is consistent with at least one report, where someone died from drinking 7 liters of water in 1.5 hours.
The mechanism by which water kills people is by lowering the amount of ions (chiefly sodium) in the blood. A condition called hyponatremia.
Coke contains four relevant looking ingredients: Water, sugar, phosphoric acid, caffeine. Coke also has carbonic acid from the carbonation, but I'll assume we're either talking about uncarbonated Coke, or that the carbonation does not contribute to toxicity (perhaps a bad assumption).
Before worrying about whether the water will kill you, let's verify that the caffeine and sugar won't kill you first.
It seems unlikely that the caffeine in the coke would kill you before the hyponatremia. The concentration of caffeine in coke is about 0.1 mg/mL, and the LD50 is > 150 mg/kg, so for the same 68 kg person, it would take about 100 L of coke to get a lethal dose of caffeine.
The sugar in coke is more deadly, but still not as bad as pure water. There are about 0.11 g sugar per mL of coke. The LD50 of sucrose is apparently around 30 g/kg. So it would take about 2 kg of sucrose to kill our 68 kg person. That is about 18.5 L of Coke.
The concentration of phosphoric acid in Coke is about 5 mM which is about 0.5 mg/mL. The LD50 is about 1530 mg/kg. Which works out to about 212 L of Coke to kill by phosphoric acid.
Now that we've ruled out some other possibilities, lets get back to whether coke will kill you faster or slower via hyponatremia than pure water will.
Take another look at the the nutrition information for Coke. Notice that Coke actually contains some sodium, about 0.13 mg/mL in fact. A drink called "Powerade Isotonic" which claims to have a proper electrolyte balance contains sodium at 0.28 mg/mL.
So given that (A) what kills you first from drinking too much water is hyponatremia. (B) Coca-cola contains a non-trivial (but still less than many electrolyte drinks) amount of sodium. and (C) other potentially toxic components of Coca-Cola, such as acid and caffeine, require much higher doses to be toxic. It seems reasonable to conclude that Coca-Cola has a lower acute toxicity than distilled water.
I did not consider osmolarity. There could be some effect here that I'm overlooking.
I did not consider the effects of carbonation (soluble carbonic acid).
For people with certain medical conditions, such as diabetes or caffeine sensitivity, Coca-Cola may be toxic at much lower doses than for other people.