Ultimately, the right answer to this question depends on your needs. On-site data centres often give organizations peace of mind knowing that they have physical control over their infrastructure and sovereignty over the geographic areas in which data is stored, something that can be especially important when it comes to sensitive personal information. They are, however, much more expensive to set up and maintain on an ongoing basis. Off-site data centres can be a cost-effective option, and they provide increased scalability as you can ramp usage up and down dynamically.
Keep in mind that it doesn’t necessarily need to be one or the other. A hybrid approach, one that blends on-site and off-site data centres, might also be a suitable path to pursue. If, for example, you can transition to storing portions of your data in off-site, cloud-based data centres, you can then re-provision your on-site resources for critical needs and workloads without needing to make additional investments in infrastructure.