The Wi-Fi standard 802.11n theoretically allows for speeds of up to 600 Mbps, but that is the total that the router offers over several channels. When you connect to a computer or device, you won't connect at the full 600 Mbps rating of the router.
When considering a 600 Mbps router, there are a host of caveats and limitations that determine how close to that speed your WiFi connection will be in reality.
The 802.11n standard was released in 2009. Since then, several new releases with greater capability have since become mainstream in the consumer market.
Internet Connection Speed
Regardless of the speed of your router, if your throughput through your internet service provider doesn't match the theoretical speed of your router, the router cannot "make up the difference." A 600 Mbps router will never deliver that speed on a network cap of 200 MBps. Upgrading to an 802.11n or newer router to obtain faster speeds only makes sense when the new router can take advantage of a speed gap in your network access.
Home Network Connection Speed
If you're primarily interested in how fast your network is inside your home (not how fast your internet speed is), then an 802.11n router would be an improvement over an older router of the 802.11 a/b/g standard. For example, if you share files between computers and devices inside your home, the faster router would speed up how quickly those files are transferred.
However, that throughput is only relevant within the network inside your home; as soon as you go out to the internet, you will be limited by your ISP speed.
Computer and Device Compatibility
If you want to get a faster router with the 802.11n standard, verify the computers and devices that will use it are compatible with 802.11n. Older devices may only be compatible with 802.11 b/g, and though they will connect and work with a router that has the newer n standard, those devices will be limited to the slower speeds of their older a/b/g standards.
2.4GHz and 5GHz Channels
Modern Wi-Fi routers have two channels, one is 2.4GHz and the other is 5GHz. The 5GHz channels offer faster speeds but have a slightly shorter range. With both channels, the farther away from the router you are, the slower your connection speed is going to be. So, if you're looking for improved speeds from an 802.11n router, you will need to factor in where you place the router to take greater advantage of the improved speeds.