For world pvp, duels, the legendary cloak is far superior because it has double the stats compared to the grievous cloak.
In battlegrounds, rated battlegrounds and arena, the stats of the legendary cloak are getting scaled down.
Legendary cloak vs grievous cloak. Comparing the two items, the legendary cloak has 63 more agility, 232 less crit chance, 119 less haste. And has 389 mastery instead of 347 PVP power from the pvp cloak.
Mastery is not a great stat for the Marksman spec (talking about hunters), trading it for PVP power is not an advantage. Having 63 more agility and losing 232 crit and 119 haste is again, not an advantage.
The conclusion is that the legendary cloak is worse than the grievous cloak in bgs, rated bgs and arena.
Compared to the tyrannical cloak, the legendary cloak is better because it has 249 more agility.
If you just play battlegrounds for fun, you can just play using the legendary cloak (because of the awesome visual effect). The difference between the stats from the two cloaks is not ground breaking.
But for arena, you should use the grievous cloak.