Yes, going to the 4K box would help, but even the 9865 (Nextbox 3.0) is much faster and usually responds about as quickly as you press the buttons. There are plenty of used ones for sale on Kijiji or similar for $40-50. Here's what you need to be aware of when purchasing used.
Since Rogers is phasing out Digital Cable and since there is very little 4K material, there's no real reason to go for a 4K box. You'll be migrating to IgniteTV "soon" (1-2-3 years?) and you may even wish to consider that option soon, although you should read through the various Ignite threads here regarding issues, self installs, etc.