Engie, Gunner, Scout (with single-target focused loadouts) do tend to perform best in dreadnought missions. Driller plays more of a support role, but can do decent chip damage and make pathways to ensure cover for teammates. There are also tactical support strategies such as fully freezing dreadnoughts while weak points are up and having a teammate do a massive burst of damage.
You can build single-target damage builds as driller with overclocks and they will work decently well, with the caveat that the weapons used for the build will lose a lot of their normal utility.