In my experience, that sort of thing can be hit and miss. There are lots of variables, in this case the transmitter power may be the biggest problem. If you have time to read reviews (and money), try and get something that has a few positive reviews. Obviously there are a few "known-good" winners at the top end of the market (Asus being the most famous), but at the lower end you may not necessarily get something that much better than what you have.
Dual band means 2.4 GHz (the old frequency range, covering 802.11b, g, n) and 5 GHz (the new frequency range for n and now ac). 802.11ac is the way in which the signal is encoded, how many stream can send and receive simultaneously, the way multiple frequency channels are used and aggregated, techniques for adjusting to interference, etc. It is "just" a cleverer way of sending and receiving data using the same set of frequencies that 802.11n uses.
The general rule is that as frequency and data rate goes up, it becomes less able to handle interference. In your case, I suspect this means you need a good quality 2.4GHz Wifi access point more than a dual band one. However, most good Wifi access points will be dual band.
