The devs have gone on record as saying that VIP chests offer at least a 10x chance to result in a Mythic as Gem chests do. We don’t know the exact drop chances, but regardless of what they are, VIP chests will be a better deal – if you only care about Legendary and Mythic drops. If you care about the other rewards (traitstones, Ultra-Rares, etc.) then obviously this doesn’t apply.
Assume, for the sake of argument, that there is a 0.15% chance to draw a Mythic from a Gem chest. You then have a 1.5% chance to draw one from a VIP chest. Your chances of not drawing a Mythic on each pull is 99.85% and 98.5%, respectively.
Let’s say you are investing 2,250 Gems into either Gem keys or VIP keys. This translates to 250 Gem keys when buying them in bulk (their most efficient), or 50 VIP keys. Your chance to get one or more Mythics from Gem chests is:
Pg = 1 - (0.9985250) ≈ 0.313 = 31.3%
Your chance to get one or more Mythics from VIP chests is:
Pv = 1 - (0.98550) ≈ 0.470 = 47.0%
So there is a marked increase in efficiency using VIP chests to draw Mythics as compared to Gem chests.