Dual band has nothing to do with speeds. Dual band means it can have one network in 2.4Ghz and another in 5 Ghz (some cheaper units make you choose which band and you can only have one running at a time).
Keep in mind that a data rate is the speed and not the actual throughput. Because of medium access methods, aggregate throughput is typically one-half or less of the availabe data rate speed. So if you bought a router that had a data rate of 600Mbps then your throughput would be around 300Mbps. But your router has a data rate of 300Mbps (so your throughput will hopefully be around 150Mbps). Also your client device will also determine your speeds (if it can't support some features you don't get to use them).
In anycase getting great speeds off of 2.4Ghz is pretty hard because of interference and you have to use 40Mhz wide channels which typical don't work well in 2.4Ghz. So you have to go to 5Ghz and use 40Mhz wide channels. Also if you use anything other than AES for security you will default to G speeds anyway. Also other factors will come into play for speed like DRS (Dynamic Rate Switching).
Also N gives you SDM (Spatial Division Multiplexing), more subcarreirs, shorter guard intervals, frame aggregation, block ACKs, Transmit Beamforming (TxBF), MIMO, STBC, LDPC, and other things. This is just a quick over view as you can go much deeper into the subject.