The outcome depends on the specific situation and "attributes" involved as well as options in the conatining comp such as continuous rasterization/ collapse transformations. There is per se no advantage or disadvantage, it's all about structuring your rendering process, but yes, in most cases the nested comps will be evaluted before the parent comp, so there is "processing delay". Anyway, this is a rather blanket question that can only lead to endless discussions, so I suggest you read the relevant help sections first and come back with more specific question when they arise. There are also other articles dealing with AE's render order e.g. by Chris & Trish Meyer in their AE books which should be partially available as excerpts. Look that up, also.
The processing time does not change, only the rendering order. I'll give you the basic rundown. After Effects makes calculations starting from the Top of the timeline and moves down. Take a look at this screenshot:
The first layer rendered is the Particle World layer. The first thing rendered is the mask, the second is the Effect Layer, then the Transformations. These pixels are then combined with the floor layer honoring the blend mode and alpha channel generated by the effects and the opacity.
In this project the Mask makes resets the alpha channel boundaries of the layer, then the Radial Blur is applied to the pixels of the layer, then the Particle World effect creates the particles. Particle World uses the layer size and not the alpha channel as the canvas for the particles so the mask and Radial Blur have no effect on the particles because they were calculated first. Then the layer transformations are applied.
There are two problems we need to solve. First, we want the Radial Blur to blur the particles so we can move the effect below the Particle World layer. The second is that we want the mask to effect the particles. We cannot move the Mask below the effects so the solution is to pre-compose the layer and apply a mask to the Pre-comp. It's how you change the rendering order.
You can also group more than one layer and pre-compose. Among other things it makes masking and applying transformations to a bunch of layers easier. When you select multiple layers there is no option to leave attributes in the main comp.
When you Pre-compose moving attributes the Pre-comp takes on the size of the original composition. Collapsing transformations extends the boundaries of the layers and also effects the rendering order of some effects. When you Leave Attributes then the Pre-comp is the size of the layer but none of the effects or transformations are moved.
The most common situation where leaving the attributes in the main composition would be useful is when that element would be shared in several compositions.