It has been suggested that I use CSS for displaying XML. I know in my heart that this is wrong, but cannot find the words to adequately convince others. Can anyone provide me with a list of pros/cons of using CSS and XSLT for displaying XML.
What your heart tells you is correct. Though it is possible to use CSS for XML, XML itself does not have any semantics. CSS is meant for the web, for HTML and for giving semantic data a (good) look.
XML is way more general then that. XSLT is was invented for transforming one data format to another (XSLT 1.0 only XML, XSLT 2.0 any Unicode data format), i.e., XML to HTML or XML to XSL-FO or another XML or text format. XSL-FO was invented for laying out XML on paper or screen and is much more detailed then CSS.
Mainly cons, esp. in the light of using XML in a browser. Skip to the overall advice below if you don't want all my babbling ;-)
The cons: it depends a lot on the context, but if you want to use XML for display on the internet, think again: don't use XML, but transform it into HTML. Then use CSS + HTML to display your data. If you use XML on the internet, no search engine or crawler, will understand the difference between <x> and <y>, but they will understand the difference between <h1> and <h2>.
This alone is enough a reason for using XSLT to transform to HTML + CSS and avoid XML on its own.
The other extremely big reason you can use: XML + CSS means defining each and every element in CSS. Using HTML + CSS means user agents already know the default layout properties for all elements. Using XML + XSLT means usually you create HTML + CSS. You should do this on server side, because client side XSLT is not very reliable and cross-browser compatible still.
(sorry, I can't find pros) Unless XML has semantics (SVG, as mentioned by another user), it makes little sense to use CSS for layout. If the layout is supposed to be semantically understood by a user agent, XML + CSS is a no-go. Text-to-speech readers have no idea what to do, WAI (accessibility) validity will be impossible etc.
Using XML makes it hard to do any client side scripting (yes, the DOM is available, but how do you tell the browser what the script-tag is? But perhaps it'll react to <script>, but hey, you need XSLT to get that tag in there) and makes it hard to make it cross-browser correct (some browsers have a hard time using XML per se). Anything HTML (like meta, title, body, script) will not be available. There's no way to add title attributes or to tell the browser what an image is (afaik).
No script in existence will work on you XML-only page (prototype.js? jquery.js? ajax? no no and no).
Anybody looking at your code will have to learn what each tag "means". Using XSLT to transform to HTML, prevents this. This extra step is beneficial and should be applied whenever you go from XML to browser display.
If your domain is SVG, SMIL, OD or anything else, you probably already know this: CSS is an integral part of the specification and should be used. This is completely different from pure, possibly unstructured, data XML.
Just for comparison: any asynchronous AJAX call (should) return XML. But any library working with it, will either interpret it as HTML, or will use XSLT or another means to transform it prior to injecting it in an existing page.
Based on the remark from the OP, we are looking at data XML (not SVG or OpenDocument) and it needs to be displayed in browsers. Accessibility and indexability are not important. But that doesn't really matter: you shouldn't use XML + CSS alone, unless you're really into some adventure and want to find out all the shortcomings of XML in browsers, want to invent every HTML tag again and define each and everything, only to give up after a while and revert to HTML (XML + XSLT == HTML + CSS).