Graceful degradation vs. Progressive enhancement
First of all, I know that this is somewhat of a "controversial" area, but in the end you do not need to agree with what I have to say, it's just my point of view. But, before we get to the subjective part, let's take an objective look at what is involved when considering these two approaches to (in this case) making web-applications.
Graceful degradation (or fault-tolerant system).
In web design, this is the basic idea that we design and write code for the most capable browsers first, then we add support for less capable browsers. An example of this is the "alt" attribute of the «img» tag. Most users will get the image, while those that browsers that do not support (or choose not to display) images gets the "degraded" text representation. The «noscript» tag is another example.
When subscribing to «progressive enhancement», you will first design and write code for the least capable browsers (like Internet Explorer). Then you'll add in functionality to enhance the experience for users with more capable browsers (like Opera, Firefox, Chrome and Safari). The linked stylesheet is a much used example of this. First you create the web-app in pure HTML (works almost everywhere), then you link a stylesheet to the page (which is ignored by old browsers), making the experience better for more up to date users. The FlashPlugin based «SIFR» method is also an example of «progressive enhancement».
Both of these practices will lead to the same result in most cases. That is, the goal of both approaches is to give the best user experience no matter what browser might be trying to display the web-application. The difference is the starting point. Where as «progressive enhancement» assumes the lowest common denominator as a starting point, «graceful degradation» assumes the opposite, starting at the newest and adding in support for less capable browsers later.
It is my opinion that the starting point of the lowest common denominator is a not such a good idea, because this line of thought will slow down the progress of new technology adaptation, especially within large enterprise environments. I don't think people in general will catch up on anything unless there is an incentive to do so. A "degraded" experience is a great incentive. Also, web-developers should in my opinion be allowed to adapt new technology as early as possible. A bunch of pig headed Internet Explorer users should not stand in the way of that. There is also the issue of security, speed and support for assistive devices. I would highly recommend the online book "20 things I have learned about browsers and the Internet" from the Google Chrome team, where you can read about why up to date browsers are important for the Internet itself.
I know what you are thinking. "Wouldn't both approaches allow for rapid technology adaptation?". The answer is of course yes...and no. You can use «progressive enhancement» and still push the limits of technology, forcing the world forward. However, to put it bluntly, that is not the intention of this approach, it's intention is to first support the slackers, then new technology. «Graceful degradation» aims at first supporting new technology, then give the slackers the content, but with a lesser experience. There's a subtle, but important difference here.
Note that «graceful degradation» has it's drawbacks as well. It is somewhat more complicated to add in "old technology" to a "new technology" project, rather than building "new technology" on top of "old technology" like «progressive enhancement» does it. But, as time goes by, a «progressive enhancement» approach will have more and more of it's foundation deprecated, while the root building blocks of a «graceful degradation» based project will become more and more relevant.