My short answer is: if you can afford it, PaaS will let you go live quicker. The long answer is: you guessed it, it depends:)
You can go a very long way with a PaaS based solution until you get to the point where you feel that it is holding you back and if your app is relatively simple you might never get to that point. Then again, if your app is simple it probably means it won't be too hard to go the IaaS way.
So my suggestion is, if you can afford it and want to go live quickly go with heroku. Once you feel you've reached the limits of heroku (meaning specific customizations or insights that you can't get out of heroku) or once you want to reduce costs start migration to an IaaS solution.
Be aware though that this doesn't mean you don't need to understand what's going on at a lower level. Understanding how heroku (or any other PaaS) solution works will help you get the most out of it at a lower cost and avoid unexpected errors. It's also a great way to start learning about DevOps while having a lot of the difficulties handled for you.