This isn't as rigorous as it should be, but may offer some useful insight into how big and small companies differ operationally.
Putting Apple aside, larger companies tend to sell larger volumes of products (even if they're MRI devices, or turbines) relative to what smaller companies can sell (obviously, in absolute terms as well). They are also able to negotiate volume discounts as well as payment terms. This allows them to finance sales through their supply chain. However, their large direct competitors are able to do the same thing as well. Competitive forces then drive prices down.
Smaller businesses, without these advantages of scale, tend to have to charge higher margins since they have to pay directly (and, if their clients are large businesses, finance the sale). Small businesses still have higher proportional costs of operation. Sadly, my reference here is a study I performed for the South African Revenue Service about ten years ago, and not available online. However, the time taken by a small business to manage admin, tax, HR is a greater proportion of revenue than for larger companies.
If the small business is a start-up with big investment from venture finance, then they could subsidise their selling price, run at a loss and try and gain scale. Funnily enough, there is a fantastic article on this by Joel Spolsky (Ben and Jerry's vs. Amazon)
For the average highly-competitive smaller company, the best choice is to chase design/quality/premium markets in order to justify the higher margins they have to charge.
And that's what makes Apple interesting as a case study. They were a small company in the presence of giants (Intel, Microsoft, IBM). They were "forced" to concentrate on design and premium markets in order to justify their need for higher margins. It almost didn't work but then they broke through. Now they're in the unique position of having gained scale but are still small enough relative to other electronics manufacturers to continue charging that premium (by volume their sales are still relatively small but their margins make them a giant).
This type of variation from market to market makes developing some sort of generalised solution very unlikely but the general requirement holds: that smaller companies must charge higher margins in order to create equivalent profits to larger companies which must gain scale through volume.