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Wait? This is supposed to be a generation change moment in GPUs and waiting a few months would probably grant you more bang for your buck.

GTX Titan Z

I think you've already answered your own question.
The 380 will play games quite a bit better at 1080p than the 370, so if you can afford it and intend to upgrade to 1080p before getting another card, then I'd get the 380.

You can compare the two here and decide for yourself

I would really wait until I saved money for a 970 than get one of those power hungry ovens.

I went from a GeForce GTX 460 to a Radeon 260X to reduce electricity consumption. AMD's video drivers are still ridiculously buggy. (There was more than a year's worth of driver releases that crashed on starting Skype, for just one example.)

Wait until you can buy what you want from NVIDIA after the generational refresh.

I'd suggest saving money for nVidia's card.

Wait for pascal or polaris.

380 :3

First things first. Check out your power supply. You'll need to open your case to do this, but no biggie if your doing an upgrade anyway.

If you have a 700W or above, chances are your already good to go. Most computers I see from stores only have 400~450W, but some of the newer cards have 600W requirements (use less then that, of course, but its to account for everything else in the computer drawing power.)

Sometimes you may need to do a little digging to find PSU requirements. No end of supposedly dedicated computer stores online or offline do not supply this information readily.

Note that the R9 380 typically has a 550W requirement, while the 370 requires 450W. I don't know about the 370, but the 380 consumes 225W.*
http://www.realhardtechx.com/index_archivos/Page362.htm

From my experience you can usually chop 50 off for Sapphire cards, since they're pretty good on power. The Sapphire version is rated for 500W, but 850W is recommended for CrossFireX.
http://www.sapphiretech.com/productdetial.asp?pid=421F760D-5247-4A25-BA5D-74A7A3139CD7&lang=eng

You'll also need to do some research to make sure your motherboard is capable of hosting the card. Both in physical terms, and software. As well as your case too, given the sheer bulk of the card. It can be easy to underestimate how big they are and have PSU Wires trailing all over the place.

Since you hadn't at time of my own post provided any other information about your computer all I can offer personally is the above advice. I hate deciding on graphics card upgrades. Too many damn factors involved. Had one once which was rated for a 450W PSU, but of course, no where did it say such when it was ordered (I was putting it in for my sister who ordered it without asking) ... she only had a 300W PSU. Needless to say, it was having a LOT of issues following until figuring out what the problem was, though that was years ago.

Consider your monitor too. Is it "Standard HD" 720p or "Full HD" for 1080p? Maybe even Ultra HD for the 2160p displays? Upgrading a graphics card is nice, but no matter how nice your card is, it's still going to look horrible on the screen if the screen cannot support the full range of display options.

Did I mention I hate upgrading graphics cards? Rather build up a new computer from scratch any day of the week and build it around a new graphics card.

The R9 380. The best card in price/performance in that category. The next step would be the GTX 970 for double the price, then an R9 Fury X for even double.

I think you better start with a new PSU

get the r9 390 its the best for the money

I just upgraded from a Gigabyte Radeon HD7850 to an Asus Geforce GTX970 OC. Before buying the 970 i waited about 5 months in which i documented myself. Atm is the best price-quality-performance you can get at a good price ... mid-budget. Never going back to AMD. I missed a lot of the features from Nvidia and now it feels great.

Seriously go for nvidia cards, not amd, they feel more optimised& compatible with most games-I've never regretted using them, but I have regretted getting an ati card.

buy 960.the performance is almost as good as 380 but with much more stability and very low power consumption.you can keep your old psu.

380 is buggy card at dx11.don't buy it.

If you don't want to wait for pascal, you could get a 390, if you're lucky, you can find one below $250 if not, yeah, stick with the 380 or get the 380x, it's only 30 bucks more

green of nvidia

Dude wait for the new GPU with Polaris (AMD) or Pascal (Nividia) you will get more for less money than a gtx960-80.
Pascal
vs
Polaris

And 1 reason why you should not buy now a GPU because you have no regular price drop because $ value (depend on your nation value).

Edit : Wait for mid-end 2016 and buy than a new gpu .... with 8 gb vram like a ps4 or xbox one. // Nex gen gpu vram :) go with time dude.

Nvidia Pascal GPU will kick ass

I run the R9 380 Dual X and have had no problems running most games in 1080p with max settings. Only a few games I've had to lower Shadings or turn off v-synch.
As for being buggy in DX11 games - I've been told this by at least 10 people - all nVidia card owners - and I have had absolutely no issues with any of my games - fallout 4 ran with max settings in 1080p and the only issues I had with that game was crashing due to the save game bug - easily remedied.
Even Ark - Survival Evolved runs great at 1080p - I only have a single card - and I've seen video's of it by people who run SLI 970's who can't seem to handle the textures that mine does.
With the performance that the R9 380's produced against the GTX 970's in the DX12 Pretests and benchmarks, I would pretty much disregard the nVidia Fanboys and do your own research into the two comparisons.
And before anyone flames me for being an AMD Fanboy, Every card I've bought for the last 12 years has been nVidia - because they were the best value for money vs performance - but AMD has been catching up and this last round of cards (even though they are pretty much just overclocked versions of the previous set) has out performed nVidia in almost every test I've seen.