Are Online Problems always harder than the Offline equivalent?

I am currently studying Online-Algorithms, and I just asked myself if online Problems are always harder than the offline equivalent.

The most probable answer ist yes, but I can’t figure the reason out why.

Actually I have a second more specific question. When an offline Problem has some integrality gap ($ IG\in[1,\infty) $ ) we know in an offline setting, that there is generally no randomized rounding algorithm which achieves a ratio $ C\geq IG$ .

Can this just be adapted to the online problem? If some fractional algorithm has competitive ratio $ c_{frac}$ can some randomized rounding scheme only reach competitive ratio as good as $ \frac{c_{frac}}{IG}$ ?

Thanks in advance.