Schema comparison is not relevant to this issue. I am looking at queries in the same database and not schema changes.
This has to do with development. I always used the toad freeware because it was excellent for development purposes (ie stored procedures, functions etc.) which is a big part of applicative side of the job of a DBA. The only reason I looked at toad Edge is because it has the tendency to freeze and crash and sometimes lose things I needed.
When running a call to a stored procedure and making changes - as you may be changing the code to fix an issue, add support for additional input variables or optimize the run time, to give some examples, the results can be different if you mess something up in the logic. The data can be slightly different based on the changes in the incoming variables (such as for example if you change parameters like order by and row limits). Sometimes something you add will slow down or speed up the runtime and you want to check back between versions. Sometimes you just need to make sure the data with one version is the same with the new version of the stored procedure. These are the main reasons why I liked to check the data and run times of previously run queries. Sometimes I forgot the parameter I got from an earlier query and wanted to go back to check that the information was correct or consistent without having to run the query over again in another window so as not to lose the data I was looking at.
I hope this explains the issue more clearly.
Additionally I find when I go some googling that the features that Toad Edge for MySQL are lacking exist in the version for SQL Server so I know that these are things that are important to other people using the software.