As a previous VP Eng and current CTO I can try and provide some insight.
It certainly depends on the size of the organization as I agree with Fred Wilson, early stage companies can have a single person handling both. At some point though, this becomes impossible. I think there are definitely grey areas here, as you find some very technical CTOs, or some CTOs that are great leaders but have not been close to the tech for some time and rely on a strong VPE.
I would say as the org gets to around 30-40 people you see the usual pattern of an experienced CTO come on board who usually has a VPE and a VP Operations reporting into him/her, separating out Engineering and Infrastructure/Operations.
At this point, a CTO starts to assume some of the non-technical burden that is required to run the technology organization. Working with HR/Recruiting on a recruiting strategy. Working with finance on budgets and forecasts. Making sure the teams are empowered with the right tools. At the same time however, there is the role of the over-arching technology strategy. What are the infrastructure, security and process goals of the organization ? Are there culture issues (technical or not) that need to be re-enforced ? Is the organization structured right? How are the managers performing ? Etc.
For a VPE, I think its a lot more of a balance of managing engineers, managing the overall quality of the code/infrastructure and being more ingrained in the day to day operation of the engineering organization. Things that might seem too nuanced for a CTO (like how are we handling our automated deployments, or leveraging Vagrant for local development?) is probably something more in the camp of a VPE. At this point, the CTO should be setting the overall technology strategy and vision (focusing on automation so we can move quicker) and the VPE should be more focused on the tools and execution to make it happen (Vagrant + Ansible + Jenkins + Docker, etc). Here, the CTO is less concerned about how its done and more concerned that it gets done and executed on in a way he/she is happy with. This issue becomes more magnified for a CTO as the Engineering organization grows to Software, Test, Data, Data Science, etc. He/She is going to need all these Engineering leaders to ensure they are executing under his/her vision properly and he/she would be stretched way too thin to get involved at the necessary levels without a proper VPE.
Hope that helps.