Should an old organisations with legacy computing go to Enterprise Cloud to get there or should pivot and go with Open Cloud like AWS and Google?

First - let's be clear. Terms like 'enterprise cloud' and 'open cloud' aren't industry standard. They are terms used by organizations to attempt to differentiate based on perceived value. Whether that is accurate or not is something I will leave up to you and other readers to decide.

If you have applications that don't scale gracefully you aren't automatically excluded from utilizing a cloud computing strategy. There are those who will try and tell you that legacy applications have no place in cloud computing - period. That is a black and white perspective which isn't helpful to organizations who are struggling with the present vs. the future. The reality is that IT has challenges like this all the time. There is a rich ecosystem of tools and services to help the more traditional IT organization move to a more on-demand cloud computing scenario. Vendors like Dome9, Cloudswitch, Racemi, and App Zero help organizations move more conventional workloads into the cloud, whether that be an on premise private cloud, a private cloud that is hosted externally, or a public cloud. Lots of factors need to be considered in that choice - data sensitivity, compute demands of your workload(s), regulatory concerns specific to your industry, and more. You are best served by finding a consultant who understands traditional IT and can help you navigate your sea of options. Avoid those who try to invent new definitions for what they do, but rather have experience with private clouds, public clouds, application migration, and performance measurement (both in the traditional data center and in cloud environments) such that you can measure your current performance and your post-migration performance for some real objective data around your efforts.