It's a litle late for you now but, for the record....
IBM Cloud Orchestrator (aka ICO and see IBM PureApplication System as well which is very similar tech). Is a system for deploying virtual machines to infrastructure configured in a 'cloud' e.g. vsphere. You can deploy those machines as single VM units or in 'patterns'. Patterns are pre-made configurations of 'well-known' topologies. Examples of those topologies include a WAS cluster or a mobile server environment which includes the whole ESB, Mobile server and WAS all in the one pattern. The advantage of patterns over a VM is that you can use those patterns to build a ready-to-go topology much quicker than creating all those scripts to install, deploy and manage all the moving parts of a single VM configuration.
BlueMix, on the other hand is a *proper* PAAS (Platform As A Service). A PAAS treats you like a user who doesn't want to know about the underlying software and doesn't want to know how to install, configure and manage the 'service' that you want. Therefore, you could consider bluemix to be more like your IT department giving you a ready-to-use database or ready-to-use Appserver. You achieve this in the interface itself by just dragging and dropping those *services* onto the canvas and telling them to deploy. The point being that you have no idea whatsoever as to how those services (DB, appserver etc ) are running, scaliing etc. As long as you pay IBM enough they will manage/scale them up for you.
Unfortunately, IBM has abused this concept of a *true* PAAS. Because, as well as allowing that *true* PAAS view on the problem they have also allowed users to spin up any-old vm image that they bring along. They also have introduced something called cloud-foundry runtimes (cloud foundry is the open-source platform that BllueMix is based on). This is bad because when I deploy my own VM's I'm now the person that has to configure them and manage them i.e. exactly what a PAAS is designed to stop me from doing !!
In addition, by adding in these options they have made BlueMix more of a one-stop-shop for deploying everything from raw VM's up to a *true* PAAS style 'service' delivery platform.However, to my knowledge (and at time of writing) - they have not enabled the ICO style 'patterns to be deployed to BlueMix (but watch this space I suspect!).
To look at these two technologies from a sellers angle..... ICO is for the "old-style" IT guys who love managing middleware whereas BlueMix is for the next generation coders who don't want to manage middleware and just "want something now where I can code".
Hope that helps !!
John.