Don't get confused by the other answers which provide more detail than you want or need. The speed of light, speed of electrons, etc. is always irrelevant (in practice) for circuits. (It can be relevant for transmission lines.)
If you include the resistance of the wires, the capacitor which connects to the voltage via the less-resistive path will get charged faster. ("Path" here means path all the way around the circuit loop...A high resistance behind the capacitor is just as effective at slowing the charging as a high resistance in front of the capacitor.) If it was just a voltage and a capacitor with no resistance, the capacitor would "instantaneously" get charged to the appropriate voltage. But thanks to resistance, you can't charge the capacitor instantaneously, because you can't push an arbitrarily large current through the wire.
Keep in mind that the charge on the capacitors is an exponential that asymptotically approaches the final value. In theory neither of them ever quite get 100% charged, they get 99% charged then 99.9% then 99.99% etc.
You can imagine the capacitors are rubber membranes like these in two parallel tubes, and you're pushing water towards these two tubes. But one tube has hair clogging it (high resistance). The membrane behind (or even in front of) the clog will stretch slowly as the water has to work its way through the hair. The membrane in the unobstructed tube will get pushed to near its maximally-stretched position much more quickly.
The length of the tube is not as directly relevant--except insofar as it affects resistance--because the water flows uniformly along the whole length of the tube. When you start pushing at one end, it "instantaneously" moves water everywhere along the whole tube. (The word "instantaneously" is an oversimplification, but unless the tube is many many miles long you will rarely need to worry about it!)