There is not a simple ranking, because shareholder influence over boards depends on several factors: voting rules, ownership concentration, the ability to nominate directors, removal rights, and whether the company has a one-tier or two-tier board.
The United Kingdom generally gives shareholders relatively strong formal powers. Shareholders elect directors and, under the Companies Act 2006, can generally remove a director by ordinary resolution, subject to the applicable procedures.
The United States varies considerably by state and by corporation. Delaware, where many large U.S. companies are incorporated, gives shareholders voting rights over directors, but actual influence can be affected by classified boards, nomination procedures, corporate bylaws, and the distribution of voting power. U.S. shareholders have also gained greater practical ability to nominate or influence director elections through mechanisms such as proxy access.
Some continental European systems work differently. In Germany, for example, large companies can have a supervisory board on which employees have substantial representation under codetermination laws. Shareholders therefore may not control all supervisory-board seats even though they elect the shareholder representatives.
Ownership structure can be just as important as the country. A jurisdiction may provide strong shareholder rights on paper, but minority investors can still have little practical influence if a founder, family, government, or controlling shareholder holds most of the voting power.
Therefore, if you are comparing jurisdictions, I would examine director nomination rights, election rules, removal rights, shareholder proposal rights, voting structure, and employee representation, rather than looking only at the country or state of incorporation.
