AMD is less expensive. Intel is better for streaming at the top end, especially if the cost is less of a concern.
With a Xeon, I don't believe you can use QuickSync... one of the bigger advantages on the Intel side, at least when Veryfast-level quality is acceptable to you. Need a QS-supported CPU and motherboard to use it, but it drops the video encoding 'hit' down next to zero. The quality is acceptable, but not stellar.
Really depends on how deep you want to go. An i5 will generally be able to swing 720@30 on most games without too many issues. 720@60 could start encountering lagged frames though, especially on CPU-intensive games.
Personally, I'd always go for an ASUS motherboard, and an i7.
It costs a bit more up-front, sure... but it saves you from having to re-buy it later if you want to go bigger, and in the interim will allow you to step to a slower encoding preset with the extra CPU horsepower just laying around, and produce noticeably better video clarity at a lower bitrate (VERY important for a non-partnered streamer; it's advised that you not go over 2000kbps, to avoid viewer-stutter problems).
The serious question is, and no elitism intended, how serious are you about livestreaming?
Casual/occasional/for-friends - Stick with what you've got now.
Regular streamer, no serious intent - AMD will work here.
Semi-serious, but unsure - ASUS mobo and an i5. You can swap it out later for an i7 if you're unhappy enough.
Button or bust - Don't screw around, save the $400, go for an ASUS/i7 combo when you can afford it.
I'd stick with the last. Trying to go on the cheap just ends up with you spending more money down the road to do it right.
My order of things NOT to cheap out on: Motherboard > CPU > PSU > Case > hard drives > video card > RAM
They go in order of what you need to get solid performance, as well as a dose of what's a PITA to swap out down the road when more cash becomes available; a video card or RAM is stupid-easy (so long as you remember to clean-uninstall the video drivers BEFORE removing the video card). The others, not so much, unless you plan ahead (like planning your SSD size down the road, and partitioning the spinning-platter drive you're using in the meantime so you can just bitwise-copy that partition over when you can afford one).