Perhaps you mean to reference Cloud Lifecycle Management instead of Blade
I would suggest that you contact your BMC sales rep. who should be able to
the product comparison you're looking for.
What component of Bladelogic are you looking? Server automation or network automation? Comparing them with VMWare is tricky. Bladelogic helps you to automate your servers and network devices. Bladelogic does provision VM using bare metal provisioning and also via VCenter. What is it that you specifically looking for?
I think that you are looking for a comparison sheet for BMC Bladelogic Client automation and VMWare vCenter Protect...
If that is the case then one of the differences would be that vCenter Protect's core revolves around centralized patch management, whereas, BBCA major competency is around management, control and enforcement of workstation configuration changes.
With vCenter you have an option to use agentless management services as well, not sure about bare metal provisioning as that has been introduced in BBCA lately.