Why play syndra when you can play lux?
Lux: 260 (2 targets)+240 (aoe) +500 (aoe)+288(2 targets) (245% AP ratio) this is with 2 passive stacks on target
1288 (245% AP Ratio)
Syndra: 230 (single target, and please don't tell me you can hit multiple people with a sphere that's barely a champion in diameter)+240(single target)+250(aoe)+900(single target) (270% AP Ratio) this is with 5 spheres, which is probably impossible to get during a teamfight.
1620 (270% AP Ratio)
So, syndra does about ~400 more damage than lux with 4 abilities most of them single target. This is assuming you have 5 spheres and are close enough to someone where your damage actually matters. Also, lux has a shield that can absorb upwards of 1k damage if across all allies. Your only hope on syndra is to get a godly 3-4 man stun off and hope your team can kill everyone in that time
TLDR: Syndra is a short range lux with only single target bursts