The S3 is an improvement with a faster processor, bigger screen with higher pixel density and mor memory, plus it's been updated farther than the S2 but it is still a 2 year old device and reaching the end of its life.
Look at it this way, if you go with an S3, expect at most a year before you get tired of it and it loses support, so you'll be in the same predicament. An S5 should give you at least 2 to three years of useful service. On an annual cost basis, it's pretty much a wash.
If you've been using the S2 without a reset since you got it, a factory reset could speed it up again for a while. If you haven't rooted, you might consider doing that and flashing a custom rom with a newer version of Android, which will perform better than the last official update (4.1). And, if you performed the updates in place (without a reset or flash) you are still using the older volume layout which will impact performance.
I keep my old S2 as a "vacation" phone. I don't worry about taking it to the pool or the beach and with a custom rom it still performs remarkably well for a device that is three generations behind the current offering.
