I did this trip once, a couple of years ago. The road south from Agadir through the former Western Sahara is perfectly good, if monotonous.
The border crossing out of Morocco is little different from Tangers, Sebta and Mellila.
There is a 'no mans land' of weaving pistes between the Moroccan and Mauritanian frontier posts. You can see it on google earth.
It's supposedly a UN zone, but we saw no personnel. The only occupants are used car dealers, bizarrely. Maybe the cars are stolen.
Mauritanian customs are far more ramshackle and intimidating. There are a few shanty huts and several battered AK47's . Actual formalities aren't very different to Morocco, but we had to pay for a visa or something.
There's a British registered(!) caravan next to the police post that was the only bureau de change we found. I was told the nearest ATM was in the Nouakchott, 1,800km away.
Once you are past customs, there's a good road to Nouadhibou.
I found Mauritania very different to Morocco, and disapointing. My stay was very brief, but it seemed expensive and 'edgy'. The beaches had rusty ships moored off them and blast furnaces behind them; Nouadhibou was dusty and depressing.