Your problem is you have an i3, which is dual core. The generation is not what's impacting performance so much as not having a quad core, especially in open world games. Your CPU does have hyperthreading but it's not the same thing as having two more cores.
You could upgrade to an i5 4690, or i7 4790. The one thing you want to be careful about, don't get an i5 or i7 that's slower than your i3, at least not by much. You want something around 3.4ghz or higher. So look at the CPU support list for your motherboard and get the Haswell i5 or i7 that is fast enough and fits your budget.
You can test your need for a better CPU easily enough. Run MSI Afterburner while you play a game. Look at the onscreen display for CPU usage. Is it on the high side, as in close to 100%, especially when the stuttering happens? if so, yeah you could use a CPU upgrade.