1. The original reason for Scotland joining with England to form Great Britain had to do with England bailing out Scotland, after Scotland got in a mess due to bad fiscal policies.
2. Scotland has been a junior partner (even if several of the greatest British prime ministers were Scots). As a non-UK, EU-member, Scotland would be an even more junior partner relative to much larger countries such as France,Germany and Italy
3. Scotland is significantly to the left of England. Indeed, without Scotland being in the UK, the Tories would have a lock on England.
4. Scotland would still be a member of the Commonwealth (and perhaps still have a resident monarch), and would still be in NATO (albeit as a minor member similar to Denmark or Netherlands or Portugal).
5. Note that the Scottish legal system, and local public administration, were never merged with that of England.