Depends on from which version the upgrade is planned.
If the application is more than 6-7 years without upgrade, most likely you upgrade analysis will show that reimplementation is the best option, more over it should be staged to ensure reasonable ROI and value to users.
But if upgrade is from let's say 7.8 to 8.1 then main challenge is to ensure proper regression testing.

I second what Mahesh said. Scope creep is a major challenge, and third-party/supporting applications introduce more variables. These shouldn't be underestimated.

If the customization is high in legacy then go in for reimplementation rather than upgrade. It also depends upon business criticality fo this application (higher the criticality more the regression you'll need).