The latter type, all day! I would argue the latter are actually great vocalists, just not pure singers in a conventional sense of having a large vocal range.
Examples: Anthony Keidis of the Red Hot Chili Peppers. A pretty limited range, but he can toggle between singing and rapping effortlessly. Also note the pure feeling he puts into ballads like "Under the Bridge," "Breaking the Girl," "I Could Have Lied."
John Lennon: Not much of a singer, even by his own admission, but he sure made legendary music. Part of what makes "Imagine" so enduring is how easy it is to sing. Anyone can sing along with him and dream big.
Another singer I'd highlight is Kylie Minogue. As a pop singer, she's outclassed by the likes of Mariah Carey in a technical sense, but no one forgets the distinctive breathy/raspy vocals she started using in the early-2000's (as heard on hits like "Can't Get You Out Of My Head," "Slow," "Chocolate.") Kylie was also known as "One-Take Kylie" at her first record label for her ability to lay down vocals without any re-do's.
Beyonce is one of those singers who definitely has a pair of pipes. But I think what's truly make her songs so catchy and memorable is other aspects of her delivery such as lyrics, vocal chips, rhythmic sensibility, and even raps.