You probably wouldn't see any noticeable difference. The clock speed is the same, though the architecture is better, so it should be somewhat better. But for the money you would spend on upgrading RAM and motherboard too, you may be better off finding an i7 or i5 for the 1155.
How much RAM does your system currently have? And are you sure it's a CPU bottleneck? (could be a heat issue, or GPU issue, not enough RAM, etc.) Run HWMonitor, and maybe prime95 to see if your CPU is throttling from heat. Also may want to run task manager while running the game, to see your CPU usage over a short amount of time (should show all 4 threads, and if its bottlenecked, then all 4 threads should be 100% all the time). Just a couple ideas.
Did you ever have good framerates?. You may consider wiping your system clean and reinstalling Windows to see if that would improve performance. (backing up your important data first, of course). At least you could find out if that helps, the free way.
Either way, if you can find a buyer for your hardware to help offset some of the cost, I would upgrade to an LGA 1151 platform with at least an i5 (so you can have 4 physical cores, rather than just two with a Pentium or i3). But if you absolutely can't afford anything but the Pentium, it would at least give you an upgrade path in the future, and *very* slightly better performance.