Both are Constitutional- but a 'Declared war' gives the President much greater leeway.
Justice Story:
"§ 1169. The power, to declare war may be exercised by congress, not only by authorizing general hostilities, in which case the general laws of war apply to our situation; or by partial hostilities, in which case the laws of war, so far as they actually apply to our situation, are to be observed. 12 The former course was resorted to in our war with Great Britain in 1812, in which congress enacted, "that war be, and hereby is declared to exist, between the United Kingdom of Great Britain and Ireland and the dependencies thereof, and the United States of America and their territories." 13 The latter course was pursued in the qualified war of 1798 with France, which was-regulated by divers acts of congress, and of course was confined to the limits prescribed by those acts. 14 "