The e8400 is near the top of the duo core family. Highly overclockable and compares pretty good to the I3. It costs more than the I3 but can be used in your existing 775 socket motherboard. The I3 uses the 1156 socket. Therefore motherboard upgrade cost involved. Here is a link to an example of the prices for the I3. The E8400 will cost anywhere from $160 to $200. http://www.tomshardware.com/news/Core-i3-i5-i7-Prices,8...
Since this has around 48,000 views, and probably a lot more are going to view this thread, here's a quick break down.
The Intel Core i3 processor is a dual core processor just like the Core 2 Duo. However, the Core i3 has a technology called 'Hyper-Threading' which essentially simulates two 'virtual' cores. Now these 'virtual' cores (technically speaking, thread but cores will be used to simplify this explanation) can be treated as normal cores, and can help with multitasking or speed tasks up.
However, some applications do not use these 'virtual' cores, and also, these cores are not as fast as a real, physical, non-virtual cores.
The Core i3 is also manufactured on the 32nm process, while the Core 2 Duos are made on the 45nm process, and the size of the Core i3 die is smaller than the Core 2 Duo E7000 and E8000 series of processors, and have better power consumption and heat efficiency.
The Core i3 CPUs are based on Intel's newer 'Nehalem' CPU architecture which is around 10% faster, clock for clock (i.e., with both CPUs at the same speed) than the Core 2 Duo, based on the older Core 2 architecture.
Overall, the Core i3 is a bit faster than the Core 2 Duo E7000 series, and slightly faster than the Core 2 Duo E8000 series in most applications.
Note that the Core i3 also has an integrated graphics chip on the CPU, and although it is not very powerful, it is more than enough for office applications. You will need an H55, H57 or Q57 motherboard for the integrated graphics to work.
The Core i5 600 series is essentially just like the Core i3 500 series, however, the Core i5 CPUs have Turbo Boost, an automatic overclocking mechanism when power is required. The Core i5 700 series are true quad cores however, and are based on the 45nm manufacturing process.