One is an Athlon II and one is a Phenom II, the PII 965 has 6MB of L3 cache and an unlocked multiplier, the 620 doesnt have either of those.
For an AMD budget gaming build i would go for an Athlon II X3 445 instead of either of those two, its clocked higher which will help and costs a bit less than the 620http://www.newegg.com/Product/Product.aspx?Item=N82E16819103872&cm_re=445-_-19-103-872-_-Product
The 965 isnt a good choice for any system as it costs $15 more than a 955 which also has an unlocked multiplier and 6MB of L3 cache.
The lower wattage would reduce the overall heat of the system, but temperatures are more dependent on your cooling than the amount of heat being released.
The 620 would be alright, it would be a bit slow for some things, the Athlon II X3 445 is quite a bit quicker and would do better in almost all games since very few use 3 or more cores.