Disregard the 965. The real debate is the i5 vs. the X4 955. The 955 is the same CPU, just without a mild factory overclock. In the US, that will save you $20-30 more.
Another note on the prices. Typically, the AMD boards are cheaper than the Intel boards. Thus, that extra $5 Silmarunya mentioned typically becomes more like $50+.
Another factor is the upgrade path. The i5's LGA 1156 socket doesn't appear to have one at this time. The i5 was introduced by Intel to compute with AMD's much cheaper offerings. Chances are the socket will disappear in a year or so.
The AM3 socket is going to be AMD's main socket for at least 2 years. That means additional CPUs and motherboards.
All in all, the i5 has better gaming performance. The X4 performs better under other conditions. The X4 build is cheaper by $75-150 dollars, depending on build choices. The X4 is more future-proof.
Both would be excellent choices. If you tend to build a new computer every 2-3 years, the i5 would probably be better, especially if you're a heavy gamer. If you tend to upgrade parts after 2-3 years and keep the main computer together, AMD is the better choice, especially if you're not a gamer. If that $1000 is a hard and fast budget and includes buying monitor, OS, speakers, and/or other stuff, AMD is the better choice to keep costs down.
All in all, you can't really go wrong with either. It's more of a personal choice than anything...