I think we would all need a little bit of clarification (at least I do) as to what exactly you are trying to do before I can truly give you an adequate answer, but my general advice is as follows!
What is your website? Are you selling something? Providing information? Answering questions?When you say "new platform" what exactly do you mean? Wordpress to Drupal? HTML5 to Magento? Or are you going as deep as switching from a LAMP server to a Linux Server running Bootstrap & NoSQL?
Depending on the size of your website and the amount of traffic there is a lot to consider, like if it's even worth it. And what your website does will drastically effect which platform you choose.
Switching from Wordpress to Drupal for example is pretty much guaranteed to change your URL unless you fiddle with the preferences. And switching from a Static website to a CMS is 100% going to do the same. You would have to spend a decent amount of time making sure every URL is the same. Remember URLs are not only important for the structure of your website, but every other place on the interwebs that links to you.
Anytime you switch a platform, regardless if it's on the top level or at the sever level, there is no way for it to be 100% seamless. Spend as much time as you can making sure you really want to make this change. Clean up as many loose ends as possible, and organize the structure of the site. Make SURE that this is the platform you NEED & WANT so you don't have to change again later down the road.
I agree with Jedi RobertFisher about Screaming Frog, It will scan 500 URLs for free. There is also Xenu's Link Sleuth. Other than that, you are gonna have to spend some time doing some good old fashion QC on the website making sure everything is A-OK!
Good Luck!
