I play both (and I got mastery 5 on Syndra before she was OP) so I can help you with your decision!
(You should obviously buy both eventually, but you want to know who to buy next.)
I'd say Ahri is the better choice to buy next. She's easier to learn and very fun to play. Her laning is pretty strong, she has really nice basic attacks (little windup), and combos are fun to pull off. She has a few cool mechanics here.
It's really nice to have sustain in lane, but remember to watch your mana when playing her (just like any champion).
Ahri can carry games, but she does sacrifice some burst for her really nice mobility.
Ahri is a pretty general, safe pick for middle lane. She's someone I am confident first picking. Yasuo is a pain, but most matchups are skill (as they should be!).
Ahri also doesn't change too much as the meta shifts. She's been in a really good spot forever (in other words, she's strong and healthy), and SSJSuntastic has always rated her really strong.
Syndra is another fun champion, but she's much more mechanically intensive than Ahri. Your positioning matters a lot more because you're more immobile, and you not only need to manage enemies, you need to manage the sphere timers too! With the rework it became a lot easier to get high-sphere count ultimates off, but it's still somewhat difficult. She has a ton of burst and she's a pretty decent lane bully, but remember, watch your mana! (Just like with any champion that uses mana.) Her basic attacks are decent, her teamfighting is pretty good as well, and she remains relatively strong throughout the game, faltering a bit lategame because of her early game bullying power.
Her waveclear is better than Ahri's.
Syndra tricks here.
She can carry games as well, but she needs to try to win quickly to take advantage of whatever lead she gets during laning.
Syndra is relatively safe, but she does have some hard matchups versus assassins. Keep your distance from them!
Syndra is pretty volatile. She's hard, and she goes from being quite good to quite bad. I'm not sure what the next season has in store for her.
Get Ahri first and Syndra next for two fun mages with quite different playstyles! :)
