no, you will not notice a difference on the first gen PCIe3 devices that come out, unless you are running multiple GPU cards like the 6xx version of the 590 which would eat more bandwidth than the PCIe2 can handel. For years I was running a 9800GT in a PCIe1 slot and was getting exactly the frame rates that I expected from benchmarks I had read. However, this all changes once you are running multiple cards, or 2nd and 3rd gen PCIe3 devices which will be out in a few years.
For every graphical interface from AGP on we have always seen standards committees move to the next version when the old version reaches a mainstream 50% or high end 75% of the system bus. Currently the 580 takes ~10 of the 16 available lanes. Each lane runs at 500MB/s to a total of 5GB/s of throughput. To exhaust all 16lanes one would have to reach 8GB/s (-10% for protocoll overhead, which is greatly reduced in PCIe3) of throughput for a single card (which the 590 is pretty close to doing, and thus the reason for moving up).
In PCIe3 each lane has a bandwidth of 1GB/s, which means that 50% is the 8GB/s we see at the max throughput of PCIe2. And assuming that they move on to PCIe4 when the mainstream reaches that threshold then we could (in theory) use a mainstream last gen PCIe3 card alone in PCIe2 with minimal bottleneck. This is technically true of our current mainstream cards being used in a PCIe1 slot, except for one important thing; There is no way you are going to keep the processor (not the bus) from choking a 560/560ti card because they simply are not fast enough to push that much raw data through with the exception of the highest end C2Quads (most of which would be on PCIe2 boards anyways). It would be like pairing today's i3 or mainstream i5 with a 590. The processor will choke the card because there is no possible way for it to push the sheer amount of data to populate all 16 lanes of throughput.
In short, there is no reason to worry about waiting for PCIe3 because if you are getting today's gaming i5K it will last for several generations of single mainstream to upper end PCIe3 cards before choking it off. If you are running or building a budget machine you would have to upgrade to keep from choking even today's PCIe2 cards, so when you get a better CPU before getting a PCIe3 card anyways. And lastly, those who build extreme systems tend to rebuild every 2-3 years anyways, so their buses will be fine. Standards boards put a lot of thought into these things so as not to jilt anyone, but also to give people something to look forward to upgrading to, and keep bringing in business for hardware companies.