The Homebrew maintainers think that linking against Apple's libraries is better, because you need to install less stuff.
The MacPorts maintainers used to agree, several years ago, and used to do just that. Then, Apple released a software update which changed some libraries and broke everyone's MacPorts installations. So then they changed their mind. Now, they think that linking against their own, coherently managed, set of libraries is better, because Apple can't break stuff.
To me, Homebrew just looks like an exercise in reproducing others' work without learning from their experiences. I don't see any advantages to it myself.
Less fundamentally, there's also quite a difference in the number of packages. MacPorts's homepage indicates that they have 18530 ports. An ls|wc in Homebrew's repository indicates that they have 2802 formulae. That said, i suspect that 95% of what people actually need is in the collection that Homebrew has.