Best way I found to solve this at the time was via SourceTree app (for mac in my case). it will automatically show you the latest changes and you can compare specific commits if you like as well.
Thought I would add this here, as did not find a good answer for this question anywhere.
Update, June 29, 2020: Based on answers from reed_do_it and scott-carpenter, went to check this and found that indeed BitBucket now have this feature on the website UI. The version i see on the site, at least for me, is what scott is showing above.
Here is the UI I saw:
- On Bitbucket site, go to any repo you have
- Select one of them and click on the file you want to compare
- Click on the Source listbox and select 'Compare'
- Select the versions you want to compare
As reed_do_it said, the URL changes with your selection, so you can send someone the link and if they have access to the repo, they can see it as well