Only option IMO is GTX 770. Nvidia's releasing a feature that will record using GPU resources soon.
From Tom's GTX 780 review: "Enabled, ShadowPlay leverages the NVEnc fixed-function encoder built into Kepler-based GPUs and automatically records the last 20 minutes of game play. Or, you can manually control when ShadowPlay starts and stops doing its thing. This replaces software-based solutions like Fraps, which exact a more demanding load on your host processor. As a quick refresher from our GeForce GTX 680 launch story, NVEnc is limited to H.264 encodes at up 4096x4096. ShadowPlay is not yet available, but Nvidia says that when shows up later this summer, it’ll do 1080p recordings at up to 30 FPS. I’d like to see it capable of higher resolutions, given earlier claims that the encoder can handle them in hardware."