Here are a few thoughts.
Maybe you could start by listing the pros and cons of each:
9 mm
Pros: Lighter, packs into tackle bags more easily, cheaper, easier to climb, absorbs less water
Cons: Less resistant to abrasion if badly rigged or something goes wrong with the rigging, probably less resistant to damage by grit getting in between the fibres, can be a bit scary when ?shiny? and new/dry as descent can be less easy to control (depending on type of descender), knots can be more difficult to untie
10?11 mm: Opposite of above
No doubt others will think of other pros and cons.
My wife and I found that the biggest advantage of 9 mm is that it makes it possible for us to do trips where we?d have struggled to carry the rope ? not so much the weight, more the number of bags needed to carry it ? using 10 mm.
I guess ultimately it?s down to personal preference ? for what it?s worth, most of our rope is 9 mm, but we find that a length of ?chunky? 10?11 mm Marlow is great for places like Lancaster Hole where the rope will almost certainly get covered in mud, which will get ground into it (to some extent).
It?s perhaps also worth considering who?s likely to use your rope ? if you?re confident of your pals? ability, then 9 mm, but if it?s likely to be used (and possibly abused) by novices, then thicker rope might be a better bet. (I posted this as the above was being posted, hence the overlap.)
I notice that Canary states that thicker rope is easier to climb, when I said just the opposite; to clarify what I meant, I find that jammers run more readily on thinner rope (especially when it gets mucky) than on thicker rope, and it's easier to get started, but I accept what Canary says about stretch.