1. Close focusing
Dedicated macro lenses can focus much more closly than equivalent focal length non-macro lenses. This results in a higher...
2. Reproduction ratio, to be a true macro lens it should offer life size repoduction, i.e 1:1. Most cheapo telezooms that wrongly claim to be macros offer a maximum of 1:4. This means that your subject can potentially fill much more of the frame with a dedicated macro.
3. Optical design
Macro lenses being primes, are generally simpler in design with less compromises, so geometric drawing is far better, non-exsistent pincushion or barrel distortion is the norm.
4. Faster max aperture
Simpler design enables wider apertures to be used, the best macros have internal focus so that the effective aperture does not decrease with close focus lens extension as occurs on some models.
5. Usually a focus limiter, cheapo 'macro' telezooms will hunt back and forth through the enitre focal range, if you are at 300mm you may as well go and have a coffee whilst it finds focus. Most decent macro lenses have close distance or far distance limiter to speed things along.
6. Lens resolution. No not your cameras megapixels, but a measure of the amount of detail your lens can resolve before it even reaches the sensor or film. Higher is better. Dedicated macro lenses typically perform very very well, far above cheapo telezooms.
You make a fair point about depth of field. Even at f11 or f16 the subject may not be rendered entirely sharp from nearest point to farthest, this is more true if you are focused very close to the subject. Stop down below f16 and diffraction starts to sap the resolution. Other problems kick in such as subject movement or available light when you use small apertures. One way round this is to use a tilt shift lens instead.
BUT, depth of field isn't everything in the macro world, sometimes for very tiny subjects or details you only need miniscule depth of field. Sometimes the seperation helps to draw the viewers attention.
If you are serious about close up work then you need a dedicated macro. No doubt about it. And a tripod. And a manfrotto micro adjust plate. And a cable release. And some patience.
If you had told me what kind of camera you were using I could have even given you some recommendations.