Almost every class is getting some serious reworking done in Legion. Even classes that aren't getting resource systems taken away or added are seeing some pretty big rotational shifts.
Mages, though? Mages are pretty much the same.
There are of course some shifts, but as a whole, Mages are coming out of 7.0 with most of the tools they had in 6.2. Given that all three specs are going to look pretty similar, I'm going to go over all of them in the same post.
The biggest change you'll notice right off the bat is that Frostfire Bolt is gone. Instead, we have a pure-frost spell called Flurry. This has a similar cast time and also slows the target, but it sends out three little bursts of snow at our target, landing in quick succession. It is still made instant by Brain Freeze procs, so it really just steps right into the part of our rotation previously held by FFB.
There are some talent shifts as well. Splitting Ice is now a talent instead of a glyph, and shares a row with Ice Nova, giving you a somewhat tougher choice. Also, with Multistrike gone you'll have to look elsewhere for good stats. Multi was always kind of derided as "worse crit," but given how you could more or less soft-crit-cap with Shatter and Haste was devalued by all the instant spells the spec has, I really liked it for Frost. Oh well.
EDIT: Something I hadn't realized is that the new Brain Freeze, affecting Flurry, now also causes Flurry to debuff the target for just over a second to act as if it is frozen. So you can actually game this so that if you cast a Frostbolt while you've got Brain Freeze up and immediately follow it with Flurry and then Ice Lance, both the Frost Bolt (which travels slower than Flurry) and the Ice Lance will now benefit from that debuff, getting the Shatter bonus. So that's different.
One big thing is that Ignite will now automatically spread to nearby targets, giving you plenty of passive cleave.
Flamestrike is also now made instant by Hot Streak, letting you work that into your AoE pretty easily.
Combustion is now a self-buff that gives you 100% crit chance - way easier to use, but perhaps less interesting.
The biggest change here is that your mastery now simply increases your max mana, instead of increasing the damage you do based on your percentage of max mana. So I suspect we're going to be seeing a lot more long-term Arcane Blast spams to do burst damage, and you'll only have to conserve mana to ensure you don't go OOM.
Still, fundamentally all three specs play more or less as they do on live. Frost is still about shattering your enemies with Ice Lance and Flurry, Fire's still about blasting the big Pyroblasts and lining up your crits, and Arcane is still about maxing those Arcane Charges (now tracked as a secondary resource, finally) to get in more damage at the cost of mana.