General question on function growth

[dyitto]

Intuitively I would say that the above functions f and g have about the same growth rate, since f simply stays one step behind g.
A function with a REAL different growth rate would be:

h(x) = x^(x^x)

So if I wanted to look into the relative growth of hyperoperational functions, then these Bachmann–Landau notation apparently wouldn't be of much use in this context.