How would I compare two SQL databases to see what may have changed during an application upgrade?

We are performing an upgrade to an application, and I need to compare the original SQL db to the upgraded db to see what has changed. How would I do this? Not sure of the best way. Is there something like a table compare or maybe at the very least do a record count of the original db, then a record count of the upgraded db. (That wouldn't give me WHAT changed, but just that there might be a different number between the two databases.)  We are a small place and have no DBA.  I am an IT person who knows a little about SQL.  What is the best way to figure out what's changed?

Thank you!