That i5 is easily 15 % faster than the Phenom II X4 965 at stock speed. For reference: the Phenom II X4 955 performs just a bit better than the Core i5-750K, and the 965 is a few percent faster (same chip, binned differently).
On any good mobo, you'll be able to overclock the 965 to about the same performance as an i5-3350p.
Both are quad core, which is more than enough for regular use. Intel i5 quad core processors don't have hyperthreading, intel i5 dual core processors have hyperthreading, and intel i7 quad core processors have it. Hyperthreading doesn't offer much benefit in gaming at all, in general it offers very little performance benefit in windows. Hyperthreading is useful if you run linux though.
The 965 (especially overclocked) will use about 2 times as much power as the i5, which will be the equivalent extra power use as a single regular desklamp lightbulb.
The i5 has faster memory access, which is the biggest difference, but the 965 has a built-in RAM controller up to 1600 MHz native, overclockable to as far as the mobo allows, and the i5 will always run at 1333 MHz, which means that the faster memory I/O of the i5 is again very relative.
If you have a motherboard with an excellent power delivery and an aftermarket cpu cooler, you can probably overclock the 965 so that it slightly outperforms the i5-3350p in some applications, but for a non-tinkerer, the i5 is probably the better choice, also because the ivy bridge mobos are very cheap now because of the platform change. You do have to know that most mobos that accept the Phenom II X4 also accept later AMD chips, so you still have a CPU upgrade path with those, and the mobos will have more features for the same price, like more fast chipset-native SATA connectors and more USB ports.
But why not get an AMD FX-6300, which is very gently priced since the FX-6350 came out, and it will outperform both the 965 and the i5-3350p, and you'll have the benefit of the upgrade path of an AM3+ mobo?