What is the difference between Xbox 360 and a Xbox 360S?

Aside from appearances, the most significant differences between an original 360 (2005-2008) and the "S" / slim version (2010) are related to the processor type, power consumption, and heat dissipation, all of which significantly affect the long-term functionality of the system.

From the table below (source), we can see that the Valhalla processor used in the Xbox 360S is the most power-efficient and therefore has the least amount of system heat. The best possible processor for the regular 360 is the Jasper; any processor revision prior to that will have higher chances of failure due to overheating.

Also, the 360S has a more sensible ventilation design where the grill is on the top of the system (vs. the back of the system like in the original 2005 design), allowing heat to dissipate naturally upwards.

I got an original No-HDMI out Xenon model from a friend for precisely the price it's worth.

Free.

That's the only way anyone should bring one home.

One way to spot the Jaspers is by looking at the label on the back. If your looking at one of the original chassis, you do NOT want one that says 12V 16.5A or 198 W. Again, unless it's free. I'd honestly recommend never buying one from EBay or Craigslist at any price, since you don't even know if the insides match the label.

From Gamestop, might be worth it on a refurb since if it's a Jasper (12V 12.1A or 145.2 W) according to the label, it almost certainly really is one. However, I'm seeing refurb bundles on the classic chassis for only 10-20 bucks cheaper than a refurb bundle on a similar S or E.

Take the S, or the E in a pinch.

I only even took the original non-HDMI Xenon for free as a Windows Media Extender point for a 20" tv I don't care about HDMI on. When it dies, it dies.