What is the difference between using Form Submission Rule and Trigger Nurture for sending out a confirmation mail?

It depends on your needs. 

Adding a prospect to a nurture offers more info and possibilities (resend the email if not opened etc), but there is a 10-15 min delay between the form submission and the first email sent by a nurture. 

An autoresponder goes out immediately, but you can't trigger a resend AFAIK. 

So if reaction time is key, use an autoresponder. This does not prevent you from also adding the contact to a nurture, you just wont be able to create conditions on the autoresponder (opened, clicked). 

Hope this helps!

To add to what Damien is saying, I'd like to add an example of a situation. Let's say you created a form promoting a webinar. If you would just like to send one email for those who have filled out the form confirming their sign up and give them a link to the webinar, then you would want to choose the autoresponder, trigger email. If you would like to send them an email about the event, a day of reminder email, and a follow up email with the recording of the webinar only if their status for attending the event was yes, then you would want to use a trigger nurture. It really depends on how in depth you would like your communications with the recipients to be. 

Absolutely. 

And if it's a support request, you definitely want to send a confirmation email right away to reassure the contact that the submission worked. 

It would be great if the delay for nurtures could be reduced. 

Absolutely. 

And if it's a support request, you definitely want to send a confirmation email right away to reassure the contact that the submission worked. 

It would be great if the delay for nurtures could be reduced. 

Thanks a lot, guys!
This really helped me out interpreting the difference between these two functionalities.

Truly appreciate when you use examples :)