Experiences will be very different for everybody. It normally stems from an anomaly whilst running Magento 1. Something that makes a change or creates an error that you might not notice. But then when you copy those issues over to Magento 2 - Which then become an issue.
Having said that, the issues aren’t always obvious and may only crop up weeks or months after your migration. You just have to be prepared. I had the luxury of a full 2 months of testing at the time, so I was able to be thorough with finding the obvious issues. We seemed to have everything ironed out within 4 months of launch.
I can’t be specific about this, as I mentioned it’s completely different for everyone. In fact, it may only affect a minority of users.
As for the migration itself, I used “UB Data Migration Pro”. At the time, there was only really the Official Tool and this to choose from. I have zero experience with other migration solutions. If I had to migrate another store I’d probably use it again. Albeit, it’s a bit pricey starting at around $399 (at the time of writing this).