I think this depends greatly on the context of the data and what your users expect to do with it. If, for example, you're dealing with financial data in tables (as in an invoice), there are obvious reasons why you'd want to preserve positional numbers/tabular figures (to allow you to compare like-with-like easily).
If information fidelity/accuracy is less important (where simple magnitude will generally suffice), using abbreviations makes a lot of sense. This is true in operating systems' representation of file sizes, where any a given folder could have files that are very large and very small.
Here's how that's shown in OS X Lion:
As you can see, this folder contains files varying in size from 689 bytes to over 3 GB. This same information, presented in absolute terms (bytes only) looks like this:
As you can see, this latter option gives a much better idea of the relative sizes of things just by their width. The issue is we don't generally talk in terms of bytes (any more); most of the files we send around are at least a few kilobytes and often larger than a few megabytes. Since people talk in those terms, it makes sense to display the information the way users will best understand it and interpret it. It's also true that nowadays (with very large hard drives being ubiquitous) we don't often have a need to do file size comparison (and with the ability to sort the list in size order, we can quickly do so if actually required).
While I know it's not your actual scenario, I figure it's worth noting that most journalistic institutions provide style guide recommendations for when to use which representation for numbers, mostly intended to ensure figures can be easily compared.
Sadly good online style guides are few and far between (they tend to be printed resources, and I don't have them with me here to quote from), but they tend to specify different rules for monetary amounts, numbers of people and percentages or other such figures.
Here's an excerpt attributed to the Associated Press:
Use 21 million instead of 21,000,000. Also: $39 million, $22.5 billion. Don’t carry beyond two decimals.