Question

How do you think what can be difference between them?

new object[][] { new object[] { "1" }, new object[] { "2" }, new object[] { "3" } }

new object[] { new object[] { "1" }, new object[] { "2" }, new object[] { "3" } }

They only difference I see is overloaded params of methods.

static void Arr(object[][] oa)

static void Arr(object[] oa)

Maybe effeciency of memory?

Answer 1

The first one is type-safe; the second one isn’t.

Both of your arrays are exactly the same, except that the second array is typed as containing objects, whereas the first one must contain object[]s (arrays). Therefore, you could write

new object[] { DateTime.Now, new object[] { "1" }, new object[] { "2" }, ... }

Whereas you cannot write

new object[][] { DateTime.Now, new object[] { "1" }, new object[] { "2" }, ... }

…because DateTime.Now is not an object[].

In practice, you should try to use the most restrictive type possible to prevent you from making mistakes.
In your case, you should use a string[][] to make sure you can’t put DateTime.Now in an inner array.