Guardian: Best single target threat. Worst aoe threat. Worst dps. Mid range for passive mitigation, cooldowns, and utility. Best snap agro. Worst mobility.
Shadow Tank: Best utility. Worst passive mitigation. Mid range on both threat types and aoe dps. Best single target dps.
Vanguard: Best aoe threat. Best mobility. Best passive mitigation. Worst cooldowns and utility. Worst snap agro.
Have you actually played and observed all of the various tanks to get here or are you just parroting what you've read elsewhere?
Guardians have the absolute worst ST threat generation. They've also got the worst "snap aggro" insofar as their ability to generate threat within a small window of time, which is one of the reasons why it's so easy to pull threat off of them in the opening volley of a fight. Of course, the entire concept of "snap aggro" is questionable at best, in my opinion, since Taunts take care of most of that, especially in the opening volleys of a fight (Throw>Leap>Sweep>(Taunt)>Sunder>Guard Slash>Blade Storm>Sunder>(AoE taunt)>Master Strike; I can generate all the threat I normally need without the Taunts but, if I'm running with a couple of the overgeared assault DPS in my guild, I just toss those taunts in at the appropriate time and, guess what, threat handled and that rotation is one of the worst for tank threat gen, when you get down to it).
Of course, Guardians also have *amazing* mobility, thanks largely in part to Guardian Leap. If you're not using Guardian Leap, it's your own fault, but, if you do use it, it's friggin' *amazing*.
You also got Shadows pretty wrong. Shadows are the *de facto* threat kings, for both AoE and ST situations. For ST situations it's pretty much down to having equal-to-better ST damage than a VG but accomplishing said damage with attacks that have high threat modifiers (Project generates 15% additional threat via talent, Slow Time and Force Breach are both high threat abilities). As for AoE, Force Breach and Slow Time are both AoEs that are high threat, which means a *lot*. Force Breach might have pretty bad damage, Slow Time is *excellent* and also has the benefit of being on a 7.5 sec CD, so it's also eminently spammable. VGs have Pulse Cannon (3 sec channel cone; nice, high damage, but it's on a 15 sec CD and isn't high threat), Sticky Grenade (15 sec CD, doesn't actually hit that hard, and is delayed so the threat benefits are kind of negligible), and Mortar Volley (hits like a truck but is on a 1 min CD; it's also difficult to use mid-fight; it used to be the king of AoE threat but then BW shrank the radius of it so you don't hit the entire pack with every shot). Explosive Surge and Whirling Blow are both terrible, so they're largely moot. VGs have decent *burst* AoE threat, but they're still drastically overwhelmed by the sheer consistent AoE threat generation of a Shadow (not to mention that their self heals generate tank modified healer aggro, so you're generating roughly 200 threat/sec on every enemy, even if you're not attacking them).
As to the question of mobility, you've seem to have VGs at the top and Guardians at the bottom. I can only presume you arrived at this juncture by looking at attack ranges arbitrarily, which is pretty strange considering mobility refers to the ability to move, not the ability to deal damage at various ranges. Even if you want to consider effectiveness at various ranges rather than actual ability to move from one place to another quickly, it's all really a wash. VGs get to use their basic attack and a long, high damage CD at long ranges, which gives them a bit of an edge in kiting, but their threat is comparatively pitiful and their mitigation takes a dive when they're not within 10m (no Energy Blast or Ion Pulse for Screen stacks), and their threat hurts a lot when they're not within 4m (Stockstrike is the single biggest, consistent, heaviest hitter they get); as to their actual mobility, all they really have is Storm. Guardians are pretty much bent over if they're not in melee with a target:at 10m, they can only use Blade Storm, Force Stasis, and Force Push while at 30m they only get Saber Throw; of course, they get to Leap at the target, so it's not like they're particularly handicapped by an inability to close with a target; for those times when they don't want to be in melee, they've got Guardian Leap, which is a stellar ability, assuming you actually use it. Shadows, while they're nominally most effective in melee, lose almost nothing at 10m (Saber Strike and Double Strike consist of *maybe* 5% of total damage dealt, which is even less of total threat), and, while they're not going to be able to generate massive threat and damage at a 30m range all the time, an HSx3 TkT with Force Potency is going to generate a *lot* of attention pretty effectively; to round them out, Shadows don't have a Leap, but they have Force Speed which means they can't close quite as effectively (it takes longer to get there and functionally wastes a GCD or 2 thanks to having no damage or threat output from it) or as often (20 sec CD rather than the 15 sec CD of the leaps) but makes up for those deficiencies by being able to be used whenever to get wherever (you don't need a target to use Force Speed).
All of this folded in, Guardians have the most mobility but the most limited functional range and VGs and Shadows are something fuzzier (VGs can Storm around more often than Shadows can Force Speed, but Force Speed has greater general utility unless you're explicitly closing; Shadows are more effective outside of their optimal 4m range, losing almost nothing in the process, but VGs have more than 1 attack on a long CD that can be used at a 30m range). The whole "tank mobility" issue has so many variables as to what actually matters when you're needing mobility that it's not really an important consideration: all of the tanks are mobile; they're just mobile in different ways for different situations.