There are a few things to keep in mind, in addition to what John said. Your current router does 300Mbps on both the 2.4GHz band and 5GHz band. If you upgrade to the AC1900, it can do up to 1300Mbps on the 5GHz band, but the 2.4GHz band is going to remain roughly the same. You see it advertised at 600Mbps maximum speed, however this is virtually impossible to achieve as it requires specific client hardware that no vendor uses as standard equipment in computers, best case scenario you can get up to 450Mbps on that radio, or up to 1300Mbps on the 5GHz radio.
Also, the faster speeds are only relevant if you are generally in the same room as the access point, as you leave that area you fall back to slower and slower speeds. Secondly, the faster 1300Mbps speeds are only on the 5GHz band, which has much less range as the 2.4GHz band.
Now that I've confused you, if you tell us what sort of wireless adapter you're using, whether it's integrated into your laptop/desktop or an external card, we can give you some better information. If all you use is the internet, then the speed of your internet plan will likely be the bottleneck regardless.