Difference between Canonical Tag and 301 redirect?

Canonical is your preferred URL. There are two ways to implement a canonical URL:

301 is implemented server side using .htaccess file
Canonical "method" is implemented using rel="canonical"

301 Redirection:

Technically 301 redirection method is used to redirect one page to another page on a permanent basis. Usually, this method is used in the following conditions:

When the information on a particular page is no longer available
Multiple pages with the same content
When some content or information is required to move to a new location (page)

Canonical Tag:

On 12th February 2009, Google has officially announced the canonical tag for webmasters to get rid of duplicate content worries when it’s your need to keep multiple pages within your website with a same content.

Rel="canonical" tag is used when you have multiple pages across internal or external websites and you want to specify to Google which one is the original one should be indexed and crawled. Usually, this canonical tag used when the any website has identical or vastly similar content that's accessible through multiple URLs and only the original one should be returned in search results.

While coming to your question, you are having a Canonical Issue with your website along with multiple index pages. I would recommend to use the 301 redirection method in solving the issue with your website:

If your website is developed in PHP then you need to make a few lines code in .htaccess file and if you are using .Net based website then you need to make a code in web.config file.

Solving a canonical issue:

Either website should be accessible with WWW OR without WWW. You need to make a redirection code accordingly in the above mentioned file.

For example, if you want to redirect without WWW pages to with WWW then - Redirect XYZ.com to www.XYZ.com

Also make sure to implement this rule for internal pages too.

Solving multiple page index page issue:

You should not require to have any index page accessible on the website:

For example: Redirect www.xyz.com/index.php or www.xyz.com/default.aspx to www.XYZ.com

Hope this helps!