A ‘server’ in the cloud normally means a virtual server not a physical server. A virtual server is a shared server not a full, dedicated server so you aren’t going to be able to get one that’s as powerful as you can get with a dedicated server. In addition, cloud computing typically virtualizes storage too. Accessing your files over a network is not going to match accessing them over a directly connected SATA connection.

If your system has a non-horizontally-scaleable component (like, say a SQL Server instance) or if you have some key latency requirements that require a very fast response calculated on a high-end CPU, then you may well be better off running those pieces on a dedicated server rather than on a cloud-based server.