The goal of having separate data marts is more related to governance, to keep data organized and where it is expected to be found (i.e. sales transactions in the "sales data mart"), and less related to performance issues.
The advantage of having a single database acting as a data warehouse is that all your data for analytics will be stored in one place, making it more accessible and easier to find. In this case, you can use schemas to implement (logically) separate data marts. You can also use schemas within a database to keep development data separate from production data, for each data mart.
Snowflake is different from traditional relational databases; given its technical architecture, it has no issues with joining large tables between different databases/schemas so you can certainly build different data marts in separate databases and join their facts or dimensions with some other Snowflake database/data mart.
In you specific case, if you have a large number of data marts (e.g. 10 or more) and you're not using Snowflake for much more than data warehouseing, I think the best path would be to implement each data mart in its own database and use schemas to manage prod/dev data within each schema. This will help keep data organized, as opposed to quickly reaching a point where you'll have hundreds of tables (every data mart, and its dev/prod versions) in one database, which won't be a great development or maintenance experience.
But, from a performance perspective, there's really no noticeable difference.