So, which is the dorkier genre name? "Nü-metal," what with that German umlaut, really only makes sense if you're talking Rammstein (which you're not), and the whole idea of singling out metal that's "nü" makes even less sense, since if you take it literally it should include any metal that isn't old (which it doesn't). "Rapcore," for its part, is probably less deceptive than most genre names ending with the suffix "core," if only because in this case there probably is at least something post-hardcore about how these lyrics are barked. But who cares, really? For music like this, having a dumb name is rather appropriate.
Rap and metal have been swapping spit, officially, since the mid-'80s -- Run-D.M.C.'s epochal "Rock Box" in 1984, to be exact, and then their next two album, plus the first Beastie Boys one and assorted Public Enemy sides (not to mention Anthrax's remake of "Bring the Noise" with Chuck D), not to mention "Babylon" on the first Faster Pussycat album -- though actually, if you want to be a total know-it-all, you could even cite "Doriella Du Fontaine," which Jimi Hendrix and Buddy Miles recorded with sometime Last Poet Lightnin' Rod way back in 1969. (More useless trivia: Some wacko calling himself The Lone Rager [allegedly Jon Z, founder of Megaforce Records] put out a 12-inch called "Metal Rap" in 1984, but good luck finding that one.)
Anyway, by the '90s, Ice-T was yelling about killing cops in Body Count, metal bands like Mordred and Riot (on The Privilege of Power, featuring Grand Mixer D.ST. on turntables!) were incorporating hip-hip-style cut/mix techniques, and eventually Rage Against the Machine and Faith No More ensured that this was gonna be an honest-to-Beelzebub genre. Korn, who debuted in 1994, are of course true nu-metal's obvious big boom. But Kid Rock's Devil Without a Cause (1998) is still too good to count.
Eventually -- maybe because Jonathan Davis' Tasmanian devil yapping was a new vocal species in its own right -- "rapping" per se wasn't even necessarily mandatory for a band to be considered nu-metal or rapcore. (Weird how that works, huh?) Yet as reviews of the two most critically approved albums below illustrate, when bands got too thoughtful and idiosyncratic, they were sometimes said to be "moving beyond nu-metal" -- or maybe critics just don't want to admit to liking any of the stuff. For our purposes, though, once you're part of the club, you stay in the club.