What was the real issue for opponents of the Constitution, especially in terms of a power struggle?

The United States Constitution came into force in 1789 after a lengthy ratification process that was opposed by the so-called "Anti-Federalists," who were motivated by a variety of issues. Chief among them, however, was concern that the Constitution would favor the power of a central governing apparatus, thereby threatening the sovereignty of the constituent states of the United States.
When supporters of ratification of the Constitution penned a number of evangelizing essays collectively called The Federalist Papers, opponents responded in-kind, describing their concerns about the predicted amalgamation of power in the federal government.
One important Anti-Federalist author was "The Centinel." The Centinel argued that the proposed government was overly complex and unbalanced and that the United States Senate was undemocratic and would be able to impose the will of small states upon the large; a free confederation of sovereign republics would be best, The Centinel argued. In his Letter I he explained,

... the all-prevailing power of taxation, and such extensive legislative and judicial powers are vested in the general government, as must in their operation, necessarily absorb the state legislatures and judicatories ... the senate ... is constituted on the most unequal principles. The smallest state in the union has equal weight with the great states of Virginia, Massachusetts, or Pennsylvania ... the President, who would be a mere pageant of state, unless he coincides with the views of the Senate, would either become the head of the aristocratic junto in that body, or its minion.

Another important Anti-Federalist writer went by the nom de plume "The Federal Farmer." The Federal Farmer argued that the proposed constitution would fail to preserve an equal division between the states and the center. In his Letter II, The Federal Farm wrote,

The constitution will give congress general powers to raise and support armies. General powers carry with them incidental ones, and the means necessary to the end.

The most prolific and important Anti-Federalist may have been "Brutus" who was possibly Robert Yates, a justice of the New York Supreme Court. Like the other Anti-Federalist writers, Brutus was concerned about the power that would be consolidated in the federal government at the expense of the states. Noting that the Constitution created itself the "supreme law of the land" Brutus caustically observed,

... it appears from these articles that there is no need of any intervention of the state governments, between the Congress and the people ... and that the ... laws of every stated are nullified and declared void ...
https://constitutioncenter.org/blog/the-anti-federalists-and-their-important-role-during-the-ratification-fight

https://judiciallearningcenter.org/the-ratification-debate/