Protip: COBRA is almost always more expensive than a comparable plan you can buy from an exchange. Often hundreds of dollars a month more expensive if you have a family.
The only problem with getting a plan on an exchange is that you may need to satisfy a deductible again. YMMV of course.
With COBRA I believe you can also pay your premium after the month it's due. This can be advantageous because you can opt to not pay for your last month before switching to another plan if you end up not using any services from your COBRA plan that month.