Socket type and hyperthreading support on some models, though I'm no expert. All you have to do is google the specs from Intel's website. The i3 isn't for gaming, but if you plan on buying new ddr3 then it's probably better to get the 1156 board over 775.
1] Dual core is an older version of Intel processors (btw, AMD also has its own dual cores) that was released in 2006. The low end versions are called dual cores (Intel Pentium E5200, 5300, etc), while the high end ones are called core 2 duos (E5700 onwards). As the name suggests, their silicon die consists of 2 physical microprocessors, both having identical specs. The dual core processors run on an interface called as "LGA 775 socket". Thus, they can run only on motherboards having this interface.
They have support for both DDR2 & DDR3 RAM.
2] i3 is Intel's latest line of "dual core processors" released in Jan 2010. There are 2 i3 models for desktops - i3-530 & i3-540. They have an architectural feature called "Hyper Threading", which simply means that each core has two threads, thus a total of 4 threads. The advantage of this is in multitasking, since each processor can allot one thread to one application. The operating system sees each thread as a physical core, so it shows a total of 4 cores (even though physically, there are only 2 cores). The i3 processors have a dedicated onboard HD video capabilities, which the older dual cores lack. Also, i3s require DDR3 RAM. The i3s run on LGA 1156 interface.