I'll take the Black Sabbath Plate,with a side of Pantera and a Black Label Society Salad.

Both genres over the years have had high and low points. A low point for metal ( the first low point) was hair/ glam metal what a steaming pile of bullshit. Now metal has the low points of american death metal and screamo. Groups such as motorhead, blue oyster cult, slayer, black sabbath, anthrax, megadeth, Iron maiden, Judas priest, Pantera, early sepultura, down, mastadon, fire ball ministery, electric wizard, clutch, super joint ritual, kyuss, sleep, neurosis, Tool, messugah, childern of bodom, and even system of a down make up for metal's short comings.
As well rap has had it's good and bad spots, such as disgraces as lil' wayne and souja boy. Talented MCs and groups such as NWA, Nas, public enemy, Ice-t, 2pac, Da Lench Mob, De la soul, A tribe called quest, Gang starr, Easy-E, Jay-z, 2 live crew, Too short, Ghetto boys, Kurtis Blow, Grand master flash and the furious 5, the roots, wu tang clan,and even early outkast make up for the bullshit that the record companies are trying to sell these days.

If one must accept the idea that bands like AC/DC and Motorhead are "heavy metal", then not all of the genre is unlistenable.

Likewise, if we're including the work of early '70s Jamaican toasters in the category of "rap", then not all of it is unbearable.

However:

I'll take door three Monty!

Easy, I prefer Metal unless I'm drunk...in which case even country sounds good.

This is simple. I don't like metal of any kind, but I will occasionally listen to old-school rap. I tend to favor the "partial" rap tunes in which the verses are "rapped", but the choruses (and bridges, if any) are sung.

This hasn't been much of a battle for me in the last 15 years or so. Metal, hands down. Rap has become overplayed, overblown trash made by trashy people and it doesn't work for them. Metal is overplayed, overblown trash made by trashy people too, but it hasn't interfered with the music for them like it has for these rappers.

Easy choice....Metal.
At its most extreme, heavy metal can be, as I once heard it described, "One guy raping a guitar and another screaming because of it". Most metal however is just good old fashioned hard rock.
Rap on the other hand is mindless garbage. Personally, I don't even consider it music.

Both good choices, They both have good drive, Good energy and they both are about Real issues. But back to a Wall, I guess it would Depend on the Artist. ODB is better than Godsmack I think. Metallica is better than Puff Daddy (or P. Diddy or Diddy or whatever the Hell he's calling himself these days.)
Really Pressed though and I would probably have to say Metal, but it Is a close race.