Easy. The component specification can handle a 1080p signal.
This is a common misunderstanding of component, that it is not capable of high definition. It most certain is! However, since it is an analog signal(versus the digital HDMI), degradation does occur, so there is loss in transmission over long cable distances. But anything in the normal 6ft range should be just fine. It also has the advantage over HDMI that there is no content protection specs like HDCP. With nearly equivalent capability, you won't be getting much different user experience with the Slingbox 500, as this makes the HDMI is somewhat of a gimmack.
The bit that is confusing regarding Slingbox though, is that I don't think any broadcaster is actually broadcasting in 1080p, only 720p or 1080i.
However, from reading user experiences and reviews, it's clear that the new boxes provide a sharper picture. I think this is because what was previously called 1080i on the Pro-HD actually wasn't any such thing. 1080i is a resolution of 1920 x 1080 but done in such a way that even horizontal lines are contained in one frame and odd horizontal lines arrive in the next frame. My guess is that Sling's 1080i was actually a progressive resolution of 1920 x 544 (which is what is displayed when you ask the Slingplayer to show the stream information) and wasn't interlaced at a higher resolution at all and was merely 544 stretched to fill the vertical space.
I reckon these new boxes just take a 1080i source running at 50/60fps and turn it into a 1080p stream running at 25/30fps.
Happy to be corrected, as this is only speculation on my part and I don't profess to be an expert!
If I'm right though, then it does call into question Sling's claim that the Pro-HD streams 1080i because this simply wouldn't be true (and is borne out by the reality that even at the maximum bitrate of 8mbps, it doesn't resemble a true HD quality picture).
Component cable can handle 1080p60.
This is a fact because it is what I'm running on my Slingbox 500 using the component input.
However, whether the Slingbox 350 can handle 1080p on component input is another story. See my thread on the 350 AV support section.
In a nutshell, the 350 basically crashes and reboots every time I send a 1080p signal via component to it. The Slingbox 500 handles this same signal (via component; everything the same) fine. I tried two different 350s and the problem is the same so (although sample size is low) it ought to suggest that it wasn't a defective device.
EDIT: The worse part of this is that if I send a 1080p signal to the old SOLO or the Pro-HD, you would simply see an onscreen message that says "No signal, You may be sending a 1080p signal" but the older generation box would not crash like the 350 does.