That's not quite correct. All stats are available on Tanks (even though you will require materia to increase Piety, and it's unknown why someone would even want to do that). The only class-specific stat now is Tenacity, which applies *only* to tanks.
Direct Hit is what Accuracy used to be, so in the same way that gear used to hold Accuracy (and some tank gear did), that same gear should hold Direct Hit now.
Tanks have 7(?) damage stats:
Vitality? - Changes max HP (and thus also HP/sec regeneration), damage effects unknown ("The calculation for attack power of jobs designated as tanks has been adjusted." is vague.). We still seem locked into using VIT accessories by class though, and since we can't exactly pick stats anymore...
Strength - Changes base damage. No change.
Determination - Changes base damage. Buffed.
Skill speed - Changes autoattack speeds, GCD speed. No change to D, but changes DPS by changing the 'PS' part. Feeds both Sword Oath and the Warrior Deliverance/Defiance mechanics, which are based on number of activations, rather than damage. Buffed as it didn't affect AAs in the past, and Sword Oath didn't use to get benefits from this.
Critical rate - Triggers Critical-based skills, increases damage. No change to critical hit probabilities, but nerf in critical hit 'potency'. So if you used to critical hit 30% of the time you still will critical hit 30% of the time, but if the increase used to be +42% damage for a critical hit, it will now be a smaller modifier of a currently-unknown value. Nerfed.
Direct hit - Non-direct hits deal reduced damage and thus reduce DPS in the same way misses used to, but unlike misses, non-direct hits still trigger combo advancement, etc. So your rotation won't be screwed, you'll only take a damage hit. It's no longer compulsory to 'maximise accuracy' as it's basically 100% now. New factor to damage.
Tenacity - Reduces damage taken (like armor), adds damage and increases healing received. Greatly buffed, parry was basically useless in the past.
Since Tenacity also has Tank-specific effects, we can essentially be quite certain that Tenacity is a relatively defensive stat and will not contribute as much DPS as any other stat (or else it would be broken beyond belief).
Critical hit rate is likely still your go-to if your skills require a critical hit to activate any effects, but its pure DPS effects will likely be inferior to Det to compensate for its benefit on procs - which may make it iffy on tanks, which don't have crit-triggered skills.
Determination is probably going to be the 'linear' DPS stat.
Direct Hit will probably have diminishing returns, but be stronger at lower numbers, but this is pure speculation.
While the exact values are unknown for now, the idea of Str > [Crit, Det, SkS, DH] > Ten from a DPS perspective will almost certainly hold.
In particular, if the balancing team is doing their job properly, damage should probably be Det > Crit > SkS, where DH's effectiveness starts out superior to Det at lower numbers and ends up inferior to Crit at higher numbers.
In general tanks will probably get enough SkS to meet a cooldown breakpoint first, then buff Det, then buff DH. Warriors will get more out of Crit than the other two as Deliverance's +crit% ability will stack with increased crit potency from the crit stat. Paladins will get more out of SkS than the other two as Sword Oath applies from autoattacks.