Go check the new
Tactica we've opened up following the codex release, we talk about all that, you're welcome to join the debates
The general opinion is the best choices for going competitive are Mars, for Cawl and the powerful Wrath of Mars stratagem, Stygies VIII for its army-wide -1 to Hit (and hilarious -2 to Hit Dragoons above 12") + Infiltration stratagem, and Lucius not for the dogma that is really weak in my opinion, but for the ability to deep-strike anything you want.
For survivability I think the -1 to Hit above 12" from Stygies VIII is better than the Graia dogma, as it helps against overcharged plasma and effects triggering on 6s to Hit like the Necron Tesla weapons. Graia trait is best for 1W models like Skitarii, so it could help them stay a bit longer but it's really focused around blocks of infantry while Stygies VIII is army-wide. Not being able to retreat without a nearby character is handicapping too I think. However their Stratagem to cancel an enemy's psychic power on a 4+ is a great tool, and the Graia-specific Warlord trait is a cool thing too that fits big infantry blocks even more.
Lucius' Dogma is really underwhelming compared to others, but their strength resides in the deep-strike stratagem that will give a much-needed mobility to your army. They also have the Solar Flare relic which is basically a free deep-strike for one of your character to help him support his army from afar.
All in all it depends on your playstyle, your local meta and the fluff you want to use for your army, not everyone needs the most competitive army, but having a nice-themed army that doesn't crumble at the first turn is even more satisfying in my opinion