It really depends on what your needs/desires are. You'll get a better value on the server resources with dedicated (more RAM, Disk, Network Speed per dollar), compared to cloud infrastructure. Additionally, you can fully dictate the software and all security settings of the server, so it can be fully optimized for whatever use is needed.
Cloud, on the other hand, is going to provide a high-availability (should be close to 100% uptime), high-redundancy service, which statistically should maximize uptime/minimize the chance of experiencing downtime. Modern cloud architecture has built-in self-healing algorithms to automatically restore your server and all data in the case of failure. There should be really 0% chance of total data loss in a real cloud environment, as your data is incrementally replicated across multiple storage mediums.
That doesn't mean you can't achieve the same results using a dedicated server. You just need to set some backup and redundancy policies yourself. If you're experienced in server administration, you'll get your best value on dedicated hardware.