Join Date: Mar 2013
Location: Canadian national, US for university
Assuming the usual physics problem metaphorical "frictionless in a vacuum" kind of thing, in this case man-to-man, tank to tank, so forth.
I think we'd crush the Imperium's military. Their infantry tactics are singularly terrible (they rely WAY too much on either static defense or overwhelming numbers at the cost of individual prowess aside from Stormtroopers).
Laser weapons cauterize their own wounds. We don't use bullets because they're super cool, we use them because a hollowpoint round will blow a hole the size of a fist through a dude, and AP rounds will cause a great hole that'll bleed badly. A lasgun won't do that.
Their air force is big, bulky, and relies on visual range to fight. The last time our jet fighters NEEDED visual range to engage the enemy was Vietnam.
Their armor is hugely ineffective- the Leman Russ' side skirts have an angle of approximately 0 degrees. That means whatever armor they have on it, the Leopard II or Merkeva's will be vastly superior thanks to the angles of the plates. The battle cannon is more of an artillery weapon than a proper tank killer.
The Imperial Guard only exists to soak up the damage while the Astartes or elite units move into position- without those elements, say battalion to battalion in the middle of Kentucky, they'd get wasted.