Assuming they are all the same grade (let's assume professional grade to simplify the question), what makes one better for one purpose or another? I understand that there are a variety to choose from: mars black, lamp black, chromatic black, etc.
Could someone tell me what the attributes of the different blacks are? (transparency, warmth, typical uses, etc)
The answer would be too broad because the different black pigments have all different characteristics as other pigments have in terms of hue/temperature, intensity/tinting, transparency, even value and so on. Here's what Winsor & Newton says about their acrylic blacks:
Ivory Black is a brown black of moderate tinting strength recommended for general use.
Mars Black is a denser, more neutral black with stronger tinting power.
Lamp Black is a blue black that is lightfast, permanent and opaque.
same (more or less) applies to oils, thus for a detailed description it's better to focus on pigment(s) rather than names as they are not universal between manufacturers. This applies to other hues more severely. For much accurate details you can refer to Handprint. And a chromatic black behaves as the pigments it's made of, so you can have more control over its attributes knowing what you've mixed.
