Company A - Issues 100 shares, currently has 100 MH/s. Withholds a percentage of profits, perhaps 30%, to fund future expansion. At the start the 100 shares are each worth 1 MH/s. With new hardware acquisitions, the shares become worth more and in theory increase in price.
Company B - Issues 100 shares, currently has 100 MH?s. Withholds just enough profit to cover power. Funds future expansion by releasing more shares at 1 share per 1 MH/s. Each share is forever worth only 1 MH/s and only increases in price when the average cost per MH/s on GLBSE increases.
Thoughts? I'd say the first company would benefit those that bought in early. However since it doesn't pull in additional funding with more rounds of fund raising it is limited on its growth rate. The second company can aggressively grow if the market is willing to invest BTC into the company. It doesn't really matter when the investor invests in the company if it continues to release shares to fund growth.
Your description of a B-type company is problematic, and is much more suitable for a mining bond than for a company. In a company, the issuer will begin with some stake as the entrepreneur above and beyond the funds he put in. This means that the total value of all shares is higher than the cost of the hardware purchased. When new shares are issued, the money raised is equal to the additional money available to purchase new hardware, which means that the ratio of hardware per share must increase (or that shares will be split if we want to keep a round number for the ratio). A successful new issue will thus result in a valuation increase for existing shareholders.
Other than that, the two types are fundamentally equivalent, up to some granularity. Investors in a B-type company can, if they so wish, reinvest their dividends in more shares to increase the worth of their stake in the company (and equivalently, A-type investors can sell some shares to maintain a given stake worth).
There's also a middle ground between the two extremes. A company can keep some of the profits for incremental growth, while issuing new shares when it's time for a significant change.
It ultimately boils down to personal preference of both the issuer and investors.