Larger 3750 stacks need to share their ring bandwidth across all the stack members, so two stacks vs. one stack would "increase" your stack ring bandwidth. Also in your diagram, you've doubled your connections between the core and distribution, which provides more bandwidth there too. So, at first glance, more stacks might provide better performance. However, performance also depends on your expected traffic flows.

Where will the traffic flow as it transits your distribtution layer? If the distribtion layer has much traffic that bypasses the core, then the increased bandwidth offered by the stack ring, even though shared, could perform better than needing to send traffic to/from the core devices or across the link(s) between the two distribution devices.

There are other issues to consider with one stack vs. two. One stack, besides being easier to manage, also helps avoid possible unicast flooding issues, avoids some spanning tree issues, and can shrink a L3 topology. (It's for reasons likes these, 6500s with VSS capable supervisors can be dual unit "stacks".)

If performance is so critical, that there's really a need to split 3750 stacks, then you might want to consider not stacking at all beyond perhaps dual unit stacks (because of the way stackwise works) or using a "better" platform. For instance, the 3750-E offers much more performance and is "smarter" how it manages its stack ring (more like a ring vs. a bus). Or, use a switch with a fabric between all its ports (e.g. 4500 or 6500).

One advantage of not using a single stack, assuming you have redundant paths, you can upgrade one stack while still passing traffic on the other stack.

(For your requirement to support 10[?] downstream access switches, and the two 6500 cores, a dual stack of two 3750G-12Ss, might be better. [Some Aggregator Template SDM resources provided by this model, useful for distribution, are slightly better too.])

BTW, I suggest you to consider dual downlinks to each access switch. Loss of one stack member would drop all the single connected access switches.

If you split the stack (2 and 3) you most likely would loose performance if compared to a 5 stacked solution.

The reason for this is that maximum per port in your design is 1 Gig and there are at most 11 switches with a combined total of 11 Gig input.

The ring itself will work with 32 gig input. ie between port to port there is no bandwith capping in the backplane even at full speed. (however you can get full speed at 11 ports)

in your scenario2 there would be a cap for 2 gig inbetween the switches.

wich could depending on your environment and how things communicate OR a cap at 1 gig depending on the spanning tree.

That said it does not mean that there is not other positive effects with splitting them, such as having them in different buildings to keep most of the network up and running even though there is a fire or electric outage.