In the US the checkpoints will be generally pretty close to the border and will check northbound traffic only. It is an immigration checkpoint but there will usually be dogs trained to detect narcotics as well as hidden people. Southbound traffic is not checked.
In Mexico the checkpoints check going both north and southbound. Southbound checks immigration documents (you can go within generally 15 or so kilometers into Mexico without documents. To go further you need to get docs). Northbound traffic is checked for narcotics. Mexican checkpoints are also routinely staffed by military as well.