ESOS is a mandatory energy assessment scheme, and SECR is a mandatory reporting requirement. The critical difference is that Emitwise is not a reporting or regulatory body. Emitwise supports suppliers in measuring and reducing emissions.
You may already collect much of the data Emitwise asks you to submit if you are reporting to SECR. That data might be useful when registering with Emitwise, where Emitwise seeks to understand your carbon maturity prior to calculating your emissions.
Additionally, if your data has been published publicly (e.g. if your organisation currently discloses emissions to the CDP), Emitwise may have already found that data and prefilled your registration form to make it easier for you.
The downside of only providing data to Emitwise that has already been calculated (and perhaps reported publicly) is that your client loses the ability to understand where your emissions are coming from (i.e. what industries). This would limit their ability to do supplier risk assessment thoroughly or to start the conversation with you and other suppliers with vendors in harder-to-decarbonise industries.
Providing purchase data enables your client to ensure consistent methodological approaches with respect to measuring emissions and comparing suppliers like-for-like.