In case you haven’t solved your problem yet, what I did was go to CMS - Pages - Home Page - Design, and then I removed the block and template for Compare, then the line regarding compare in the second reference.
Next, I had to edit the cms in the download by going to shop - app - design - frontend - default - base - default - layout - catalog.xml
In this file, find the one line about compare in the reference tag named “right” and delete that, too.
All you have to do from there to get to see the change is refresh your cache on Magento and your browser.
Worked for me, hope it works for you, too!
*I would also suggest that any changes you make are done in folders of your own. In my case, where I told you to go to “base”, I have my own file started there so any changes I make won’t affect an upgrade. Just keep all the folders titled the same expect your own section, copy what files and folders you need to change, and only change on your own files. Sounds confusing to explain, but there are plenty of tutorials to help you out.