What is the best workspace color profile to use while designing for billboard Ads in both Illustrator and Photoshop?
The one that the provider gives you.
In case the provider does not give you one, try using a generic one like Fogra 39.
I mention this because digital print can hold a saturated Total Ink Coverage (TOC) and this profile uses a 330%
But probably it is a good idea to send a small sample using a couple of different profiles and see which one you like most.