I think that you are missing something...
When you say that copy a comp, I think that you are copying a layer.
Pay attention to separate what a comp is, and that comp working as a layer.
If you select your Comp1 in the timeline and duplicate it, then you haven't a second comp. You have the same comp working as two layers.
But if you select the Comp1 in the bin project and duplicate it, you have a Comp2 and then you drop it to timeline. In this way you have 2 'real' comps independently.
You can change all the content of the Comp2 without any change in the Comp1.
Ok, now suppouse that you have in the bin project a Comp1 and a independent copy called Comp2.
And in the MainComp timeline have only the Comp1 (is working as a layer) with some settings.
Then you want to have there the Comp2 with the same settings,attributes, keyframes, etc of the Comp1.
So, you duplicate your Comp1 IN timeline (like you are doing right now, making a duplicate of the layer, not creating a new comp) and then replace it by your Comp2.
You just need to drop your Comp2 from the bin to the Comp2 in the timeline maintaining pressed alt.
That will replace the content of the layer (and your content is a comp), but will maintain the adjustments.
Sorry about my english, I wish this words helps you.