I'd say black will absorb more, providing that surface material and texture are the same.
It might be the same tough at certain frequencies. Like certain nm Green will match certain nm Red as opposites.
I'd be interested to hear what other members have to say.
There's no correct answer, but black is the better candidate. The actual answer is "not enough information" - but no one likes to hear that, do they?
"Black" and "Red" are just generic terms in this context to define a range of black-ish and reddish hues and shades. When you get nitty gritty with it, the "black" object you mention will have a absorption vs. wavelength relationship that may looke very different from another object that also looks black. Same with red. A black object absorbs most of all visible light - a red object absorbs more green and blue wavelengths than red.
So every black and every red is different and one black may beat out one red, or vice versa. I've had a 10W 808nm laser that couldn't do anything to bright white paper, but just the faintest shade of gray (enough so that we'd normally call it white) would quickly go up in flame.
So yeah, no definite answer unfortunately. Chances are that the black will absorb more though.