As someone who has a chrono and a mirage, I can break it down for you:
Chronomancer has a shield as the elite weapon. At its core, it will provide two things: slow to the targets and alacrity (which speeds up cooldowns, the opposite of chill) to you and your allies. There are a few traits in chrono that allow your phantasms to have another attack (after a 1.25s delay or so), allow your clones to superspeed during shatters, and providing quickness per shatter. Each well also has its own utility. The heal well strips conditions and heals on finish; the elite well does a knockdown, float and pull which does considerable breakbar damage (though not as close as the breakbar damage you can do with the humility signet). It is more effective towards concentration-moderate/heavy classes such as Commander's, but provides options for other power builds.
Mirage, on the other hand, has an axe as the elite weapon. At its core, the mechanic is known as "Mirage Cloak" which gives you (and with a trait, your clones) an 'Ambush' attack that does something depending on the mainhand you use. For example, scepter causes you to launch a barrage of bolts that cause either torment or confusion on hit; greatsword's beam splits to nearby targets. However, the Mirage's dodge is altered that instead of evading in your current direction, it activates the Cloak, which doubles as an evade mechanism. All of Mirage's Deception skills are geared to work around the Cloak, and grant some measure of mobility while staying focused on your target. With the right setup, condition damage-geared Mirages can deal a great amount of torment/bleeding, as well as confusion stacks (this is my setup); however, there are strong power-based setups as well, but requires a bit more skill.
Mirage requires you to remain on the move in order to be effective, because the dodge mechanic has changed. Chronomancer, on the other hand, provides lesser damage options, but your support options are increased and it's a bit easier to handle. You can get a working Chronomancer after the first traits (Adepts) are unlocked, but it requires a few more hero points than working Mirage. HOWEVER: both setups allow for melee and ranged options -- Mirage condi works with staves, and chrono power works with greatswords.
Chrono also has an extra shatter (see Donari's post), but with the new shatter, it gives you a few seconds to spend some heavy cooldowns before you "revert", causing those skills to be useful again. Extremely useful if you're either trying to maximize alacrity, or if you want to double-shot the gravity well.
If you're looking for just dealing raw damage, you can go either way. But I suggest putting some investment in Chrono before your investment in base Mirage, so you have a fallback in case Mirage isn't for you.
