This shouldn't be too tough to tackle, I'll walk you through the basic steps that I would take.
My basic approach would be to take a form of said checkboxes and submit it to an action designed to handle them in the way described, like so:
Create a new route to use for all of this. Take a look at 2.10.2 Adding Collection Routes in the docs (assuming you are using resources). Maybe call it something like "compare".
Use a form not backed by a model to hold your checkboxes and labels (1 of each for each product) - it should post to your new route.
In your controller, add the action for your route. This action should fetch the ids passed in by the form from the params and load the relevant products (remember that find can take an array of ids, so it should be pretty easy).
Finally, add a view for your new action, with the relevant logic to present your comparison.
You can easily come in an backfill this with javascript, but it is not required. Honestly, it would be more useful for adding a little extra panache, like disabling the button and showing a spinner, or something, than a full-on javascript submission, which doesn't really buy you anything in this particular case.