Alrighty, here are some general ideas
You're going to definitely save on power consumption going to a new intel CPU, each recent gen of Intel CPUs have become more and more power friendly. That being said, the CPU isn't going to be your main power drain, it's going to be your graphics card, so where you go with that is all the difference in the world.
Going from an older i5 2500k processor to a newer i5 4670k dropped max power consumption by only about 10-20 watts, which is still nice that you're actually seeing a decrease in power consumption corresponding with an increase in computing power. But you really aren't going to gain a ton of power savings with a new processor(the old ones really didnt use that much power, compared to overall system consumption), unless you have an original high-end i7 or something that really chews up a lot of juice(like an i7 970 or something)
The video card will be where the biggest variance happens
I assume you probably have something like an AMD 6950? Thats about a 4 year old card, and there wasn't a 6900 model card(they were 6950s, 6970s, and 6990s in the 6900-series)
At max power(gaming) a 6950 requires 200W, a 6970 requires 250W and the monster 6990 requires 375W.
For new cards, you will want to go Nvidia, as Nvidia cards are very power-friendly compared to comparable AMD cards. Neither really has an edge over the other in overall performance, but Nvidia definitely has the edge in cooling and power consumption.
A slight upgrade to your existing 6950 would be an Nvidia 750Ti(it's actually comparable to the 6970 card), its a cheap, mid to low range card nowadays(costs about $150) but only uses 60W at max power. So thats either a 140W gain for slightly better performance over your 6950, or a 190W gain over equivalent performance to a 6970
Now all of that sounds great, but a 750Ti isn't a card that you're going to be happy with for several years. Its decent now, its probably a little better than what you currently have, it'll run new games at 1080p resolution on medium/high settings, but its going to really lag behind within a year or so, you'll be wanting to upgrade it fairly soon if you go that route.
If you want a video card that is going to last you minimum a year with good performance(high/ultra in new games at 1080p) and even longer if you're ok with medium/hgh settings, you're probably looking at something like the Nvidia 770. Now that's a great card, a HUGE upgrade over what you have currently(look at it compared to a 6970 here:
AnandTech | Bench - GPU14), but it also maxes out at about 230W of power, so its right in-between a 6950 and 6970 in wattage. So at this point, the small gains you would make with a new processor are given back with the video card. But you're talking a 2-3x performance gain for basically no more wattage. Thats pretty nice.
Now, all of that being said, you could build a new PC, it's going to have a better processor, much better video card, but probably not really use less power(but it shouldnt use more), but you might see some nice gains in heat output though. The newer Intel processors can run really cool even on stock cooling, and even better with not much more than a $20 aftermarket heat sink upgrade. Newer Nvidia video cards are probably also going to have better heat dissipation than your old AMD card(I honestly like the Nvidia stock blower fans, but there's a lot of third party 2-fan cooling systems that work well too, every card is a little different), so while you aren't really saving any direct money due to lesser wattage, the damn computer probably won't heat up your room as bad as the old one did, saving on some AC costs there.
Hope that helps with some ideas for getting started.