I think the usual factors would come into play, however if your copy is more targeted towards "blue widgets", you should have a higher ctr, lower cpc than your competitor, who is advertising more generic "widgets" etc (as long as someone was searching on blue widgets)
If a competitor is bidding on term widgets (with broad match), and i am bidding on blue widgets, both our ads would show up for term blue widgets, but would i have any advantage (cause my bid is more specific for that term) or would position be decided just with the usual (bid price,quality score,account history...)?
The only advantage is that you would have the opportunity to customize your offering to a user looking specifically for "blue widgets". For instance, including the term 'Blue Widgets' in your ad, describing your wide variety of colors or shades of blue that you offer, etc.
Outside of that, your ad is given an equal opportunity against all other ads. If a lesser targeted ad or keyword, like 'widgets' on broad match, can still appeal to users more your more targeted version - then, the "advantage" is for not.
