When First Order launched the Starkiller, it was General Hux's order, Ren was in his warship. I wonder which of those two has higher rank in the First Order?
According to canon, neither.
Together with Captain Phasma (despite her simple "captain" designation), Visual Dictionary says they are about the same in pecking order. V.D. calls them "triumvirate", a term borrowed from co-leaders in Ancient Rome.
This seems fully
stolen mirroring Episode IV, where Vader and Tarkin are similarly situated (Top Leader's right-hand "Dark Jedi" acolyte/enforcer on a special mission vs. top commander - although Tarkin was a Moff and not a General, because Empire was structured differently from First Order which seems to not have any civilian structure mentioned in canon at all).
Please note that Disney clearly liked that "equal" idea between Vader and Tarkin, because they explicitly made James Luceno strongly reinforce it in the expanded dynamics between them in the new Disney canon novel "Tarkin", with Palpatine himself explicitly encouraging it.
This parallel explicitly noted in The Force Awakens Visual Dictionary:
Kylo Ren exists outside the formal command structure of the First Order, and has a direct link to the shadowy Supreme Leader who is ultimately in charge of these forces of darkness. It is with palpable tension that the upper command of the First Order contends with Kylo, as his agenda always trumps military objectives. In this way, Kylo's placement within the hierarchy resembles that of Darth Vader in the old Galactic Empire. This is entirely by design. (Page 25)
This dynamics is confirmed in the Foster TFA novelization, where we see the usual "trying to one-up each other in front of Supreme Leader" dynamic between the two, when they talk to
the Wizard of Frank Oz Snoke's giant hologram (and even earlier when they bicker about the map's existence aboard the Star Destroyer).
CLARIFICATION: While Phasma is a part of triumvirate, she is still line-of-command subordinate to either Hux, or sometimes Ren (on Jakku, in the novelization, we have
“Your orders, sir?” she murmured line).