I believe that I may be the first person to have realized that compared is a preposition. It is not listed as such in any of the dictionaries that I consulted, and you may very well be wondering how compared could possibly be a preposition. Let me try to explain.
Brett's argument starts with the observation that sentence-initial participial adjuncts are often felt to be "danglers" when not predicated of the subject of the following clause.
Fearing a massive lay-off, there was a general sense of relief when the boss announced there would be no new budget cuts.
In contrast, prepositional-phrase adjuncts don't have this problem:
After a massive lay-off, there was a general sense of anger.
He then observes that what seem to be past-particle adjuncts with "compared to" behave in this respect more like PPs:
Compared to ICS alone, there was a significantly greater improvement in FEV1 with the addition of LABA.
This is a valid argument, but not a new one. CGEL discusses it in chapter 7, section 2.3 (pp. 610-611);
For the most part, verbs are clearly distinguishable from prepositions by their ability to occur as head of a main clause and to inflect for tense. There are, however, a number of prepositions that have arisen through the conversion of secondary, non-tensed, forms of verbs:
 i [Barring accidents,] they should be back today.
ii There are five of them, [counting/including the driver.]
iii [Pertaining to the contract negotiations,] there is nothing to report.
iv [Given his age,] a shorter prison sentence is appropriate.
The basis for analysing the underlined words here as prepositions is that there is no understood subject. This is effectively the same criterion as we have used in distinguishing prepositions from adjectives: prepositions can be used in adjunct function without a predicand, i.e. and element of which they are understood to be predicated. The preposition counting in [ii], for example, is to be distinguished from the gerund-participial verb-form in:
 [Counting his money before going to bed last night,] Max discovered that two $100 notes were missing.
The boundary between the prepositional construction  and the verbal  is slightly blurred by the usage illustrated in:
 i [Turning now to sales,] there are very optimistic signs.
ii [Bearing in mind the competitive environments,] this is a creditable result.
iii [Having said that,] it must be admitted that the new plan also has advantages.
These differ from  in that no subject for the underlined verb is recoverable from the matrix clause. They are similar to what prescriptivists call the 'dangling participle' construction illustrated in examples such as *Walking down the street, his hat fell off, ungrammatical in the sense where it was he, not his hat, that was walking down the street. Unlike the latter, however, the examples in  are generally regarded as acceptable. They differ from the prepositional construction in that there is still an understood subject roughly recoverable from the context as the speaker or the speaker and addressees together.
In his second post on the subject, Brett adds some other examples, as well as a persuasive new argument:
Another piece of evidence comes from coordination. Typically parallelism dictates that we coordinate only like with like. It would not typically allow us to coordinate a PP with a VP. In the following sentences, however, we have a PP coordinated with a phrase headed by 'compared':
- Americans live very well, both by historical standards AND compared to other people in the world today.
- A major finding, however, was that emissions at the four sites differed greatly both between sites AND compared to national trends in emissions between 1970 and 1990.
At least, this shows that the "compared to" phrases are serving as adverbial adjuncts in parallel to the <i>by</i>-PP. A participial phrase that is clearly in apposition with a subject doesn't generally conjoin with adverbials this way:
*Unexpectedly and counting her money, Sally found $100 missing.
*With a wink and talking on his cell phone, John ran out the door.
(Those of you interested in the phenomenon of "dangling modifiers" may wish to join the Fellowship of the Predicative Adjunct, though you should be aware of the Fellowship's credo that this is a matter of etiquette rather than grammar.)