I have a sort of a conflict with my company's Security Lead Engineer. He says that Remote Desktop Protocol (RDP) is not secure enough and we should be using TeamViewer instead. We use RDP not only to access local resources inside our corporate network but also for the access to resources (running Windows 2012+) in cloud hosting. 

In both the scenarios how secure is it to use RDP?

I believe that Teamviewer is a proxy service for tunnelled VNC connections. Hence, the first security consideration with regard to that service is that it is MITM'ed by design. There have been suggestions that the service was compromised a couple of months ago.
(Note that although VNC uses encryption, the entire exchange is not, by default, encapsulated - but it's trivial to setup a SSL/ssh/VPN tunnel).
Next consideration is that it means installing third party software on your systems - but then if you're running a Microsoft platform then you're already running software from multiple vendors which is probably not covered by your patch management software; keeping software up to date is one of the most effective means of protecting your systems.
As long as your RDP connection is using SSL, it should be at least as secure as Teamviewer, and IMHO, a lot more so.
