I currently performing frequency analyses on oil storgae
tanks. I did a comparison between a solid model and a shell model.
The solid seemed to be more stiff and the natural frequencies do
not correlate to the shell's frequencies and mode shapes. Can you
maybe explain the reason for the difference and which model will be
the best to use.

Shell elements are well suited for thin structures. They reduce the computation effort and maintain accuracy for thin structures.

Other quesitons:

1. What is the ratio of "next largest length" to thickness? nextLargestLength/thickness

2. What is the ratio of "largest length" to thickness? LargestLength/thickness

If you your up in the hundreds to one range or more, just use the shell elements. I am unsure of where the shell elements breakdown exactly. I will have to look into this in the future.