True. But they both apply to the federal government. Look at the Sixth Amendment which provides with unmistakable clarity:
"In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury (...)" The language is as general as it gets - "In all". According to your reasoning such language should apply to both the United States and the several states. Yet Madison proposed an additional (eventually rejected) amendment which would provide:
"No State shall violate the equal right of conscience, freedom of the press, or trial by jury in criminal cases"
If the Sixth Amendment applied to both the United States and the several states than why did he propose an additional amendment which would restrict the states? Did he like repeating himself? Or was he incapable of understanding the true meaning of the BoR? Surely such distinction must mean something...
You left off the next part of the Sixth:
...of the state and district wherein the crime shall have been committed
In other words, this is a mandate to the states as well.
My position stands. IMO the Second was sandbagged by early SCOTUS politics over state powers, just as the 10th has been sandbagged ever since the days of FDR.