Very late to the party, but as someone who ran a bunch of 3E, and a fair amount of d20 Modern, Grim Tales, and Mutants & Masterminds, I am really enjoying 13th Age a ton. As others have said, combat is simple and fast, but gives folks a chance to do cool things, and the martial classes, while simpler than the casters, don't feel unpowered -- scaling weapon damage is great for that.
Pros: Shared Narrative
As players get more comfortable with tossing out times they want their icon relationships to pay off ("Can I cash in this 6 Positive I have with the Diabolist to have this demon guarding the control panel be an awkward ex-boyfriend?"), the games can take more hard left turns, which at first seems scary... and is then kind of wonderful. As the GM, there's no more expectation of me making a novel that I have to cleverly trick my players into going through. I can make rough outlines for encounters and things I plan to have happen, and when they throw a wrench in the gears, it's not a jerk player move, it's FUN, and I can roll with it, and we can all have fun improvising a bit. Rewarding a player for coming up with a good use of One Unique Thing or an Icon die is just FUN.
I've found that the let's-play stuff does even more of this. Each player takes turns establishing part of a room that you want to use for a cool battle, or each player describes part of the party's progress through a dungeon (when you want to get through it quickly instead of charting each ten-foot step).
I have players that range from "Never played a pen & paper RPG before" to "played a ton of 3.5e and other games and can talk knowledgeably about systems." Everyone seems to like the system, and simple classes like the paladin and barbarian are great for new players to get comfortable with.
Pros: Simple Enemies
Enemies use much more of their own AI to determine how they act, which lets me as the GM fling down a lot more enemies at once without bogging games down. Rather than having a lot of abilities, enemies usually have just one or two, plus other effects that automatically trigger in key circumstances. I've heard people complain about this making enemies too simple, but honestly, I can always complicate 'em if I want 'em. Starting them simple lets me add complication where I want it, like the designers do in their let's play adventures (where monsters use special abilities specifically where it's plot-important).
Cons: Improv-Friendliness Required
If you aren't comfortable changing things on the fly, 13th Age could easily stress you out. If your players are shy, it can start to feel like you're pushing them to get them to talk more, and if your players are glory hounds or jerks, One Unique Things and Icon Dice give them excuses to play into those bad behaviors. This is a game that assumes that people are playing this because they are friends in real life, and are there to give each other grief but ultimately work together and have a good time. That includes players and GMs. While 3E ad 4E often felt designed to protect the players from a mean GM and the GM from powergaming players, this game pretty much says, "Here's some stuff that is inherently unbalanceable. Hope you're all mature enough to have fun with it instead of being jerks." That is definitely not for everyone.
Anyway, I hope you have fun with it!