As a familiar counter-example, a process like the thermite reaction is "enthalpy driven". The enthalpy change for that reaction is -850 kJ/mol and the entropy change is -41 J/mol·K. Since the entropy change in the system is negative, something is required to make the entropy change in the surroundings compensate for this if the process is to be spontaneous. That something, of course, is the large release of heat.

We might say that spontaneous exothermic processes are always "enthalpy driven" because we can be sure the entropy in the surroundings will increase since heat is being transferred to them. Again, that's at least part way to increasing the entropy of the universe.

In the three exothermic heats of solution measured, the entropy was also increasing in the system (dissolving a solid in a liquid....). These kinds of processes might be considered as both enthalpy driven and entropy driven since both changes favor spontaneity.