What are the differences between these two Apple TV models

The original Apple TV (out of box) preferred to treat your Apple TV like an iPod. It wanted you to sync your video from iTunes and had the following limitation:

H.264 and protected H.264 (from iTunes Store): Up to 5 Mbps, Progressive Main Profile (CAVLC) with AAC-LC audio up to 160 Kbps (maximum resolution: 1280 by 720 pixels at 24 fps, 960 by 540 pixels at 30 fps) in .m4v, .mp4, and .mov file formats

iTunes Store purchased video: 320 by 240 pixels, 640 by 480 pixels, 720 by 480 pixels (anamorphic), or high-definition 720p

MPEG-4: Up to 3 Mbps, Simple Profile with AAC-LC audio up to 160 Kbps (maximum resolution: 720 by 432 pixels at 30 fps) in .m4v, .mp4, and .mov file formats

The new Apple TV has identical requirements as that of the new iPod touch and iPhone 4:

H.264 video up to 720p, 30 frames per second, Main Profile level 3.1 with AAC-LC audio up to 160 Kbps per channel, 48kHz, stereo audio in .m4v, .mp4, and .mov file formats

MPEG-4 video, up to 2.5 Mbps, 640 by 480 pixels, 30 frames per second, Simple Profile with AAC-LC audio up to 160 Kbps, 48kHz, stereo audio in .m4v, .mp4, and .mov file formats

Motion JPEG (M-JPEG) up to 35 Mbps, 1280 by 720 pixels, 30 frames per second, audio in ulaw, PCM stereo audio in .avi file format

As for how it works, while nothing hard has been released from the UI screenshots released items from the internet (iTunes store, YouTube, Netflix, etc.) will stream from their respective sources while your photos, music and video streams directly from iTunes or from an iPhone, iPad or iPod touch (via AirPlay coming in iOS 4.2)

Basically you have to decide what is most important to you. Do you want to have the widest range of content offerings(Roku), or the best compatibility between other Apple devices and software(Apple TV)?

The Roku box for example can play Hulu and Hulu Plus. The Hulu service is in very high demand and a very good content stream for the Roku. The Apple TV at this time will not play it out of the box, although it can be hacked to do so.

The biggest advantage that the Apple TV has is if you own or plan to use an iOS device in conjunction with it. For example, you can use AirPlay to stream music, photos, video, and apps to your Apple TV. This can be very handy in many situations. If you don't already have an iPhone, iPad, or the like - and don't plan on getting one anytime soon, then this shouldn't be a big draw.

The Apple TV also works flawlessly with iTunes. For example you can use iTunes Match then stream the audio to your Apple TV very easily. Roku can do some similar things with iTunes, but is does not have the same level of integration.

Overall, both devices have benefits and downsides, it just depends what you think your primary use will be and what hardware ecosystem you have. For more detailed information I would take a look at this review that compares the two.