Except, of course, that the slaves weren't taken "for public use." The United States didn't seize them. It freed them. That might be a distinction without meaning to someone who has all his capital tied up in owning human beings, but it is a difference.
Again, perhaps you can enlighten as to specifically what clause of the Constitution grants the executive or military the power to seize private property without renumeration?
From the Emancipation Proclamation; "Now, therefore I, Abraham Lincoln, President of the United States, by virtue of the power in me vested as Commander-in-Chief, of the Army and Navy of the United States in time of actual armed rebellion against the authority and government of the United States, and as a fit and necessary war measure for suppressing said rebellion,"
The decision in the Prize Cases goes on at length about the right to seize property of enemy belligerents in internal or external war. Here's a sample: "Wherever private property is taken or destroyed, it is because it is of such a character, or so situated, as to make its capture a justifiable means of coercing the power with which you are at war."
But in the end it pretty much comes down to this: If you want the protections guaranteed in the United States under the Constitution, you probably shouldn't go around renouncing your allegiance to it or making war on it.
Until Kelo the use of eminent domain always applied to public use. Regarldess of that decision, the Constiution is silent about takings for private use, or for simply seizing property at will - the power was not delegated to the federal government nor executive. Whatever power Lincoln claimed to exercise, he only possessed it as Dictator-in-Chief.
But in the end it pretty much comes down to this: If you want the protections guaranteed in the United States under the Constitution, you probably shouldn't go around renouncing your allegiance to it or making war on it.
But in the end it pretty much comes down to this: If you want to claim that the States had not seceded, and were still citizens of the US, then their Constitutional rights are guaranteed. See ex parte Milligan, a 9-0 slam against the powers exercides by the President, authored by his friend Justice David Davis. And that was a friend that offered bribes (cabinet positions to two delegations) to those that voted for Lincoln in convention.
Lincoln is at odds with his own Lieber Code, Article 38 stating, "[p]rivate property, unless forfeited by crimes or by offenses of the owner, can be seized only by way of military necessity", and even then, "the commanding officer will cause receipts to be given." Receipts, so that the owner may be indemnified.
I'd also stated that the Supreme Court had ruled before the war that measures such as Lincoln claimed were illegal:
There are, without doubt, occasions in which private property may lawfully be taken possession of or destroyed to prevent it from falling into the hands of the public enemy; and also where a military officer, charged with a particular duty, may impress private property into the public service or take it for public use. Unquestionably, in such cases, the government is bound to make full compensation to the owner.... Our duty is to determine under what circumstances private property may be taken from the owner by a military officer in a time of war. And the question here is, whether the law permits it to be taken to insure the success of any enterprise against a public enemy which the commanding officer may deem it advisable to undertake. And we think it very clear that the law does not permit it.
Chief Justice Taney, Mitchell v. Harmony, 13 How. 115 , 134, 138 (1852)
A position reiterated by yet another Supreme Court decision:
"We fully agree with the presiding justice of the Circuit Court in the doctrine that the military should always be kept in subjection to the laws of the country to which it belongs, and that he is no friend to the Republic who advocates the contrary. The established principle of every free people is, that the law shall alone govern; and to it the military must always yield. We do not controvert the doctrine of Mitchell v. Harmony, reported in the 13th of Howard; on the contrary, we approve it."
Justice Field, Dow v. Johnson, 100 U.S. 158, 169, (1880)