What is the difference between the following sentences:
If they have the same meaning, in which circumstances would it be better to use each one?
They have rather different meanings, depending on what counts as "meaning".
They both assert the same thing, under the same circumstances.
But their connotations are quite distinct.
Although you are in possession of a valid visa presupposes that you have a valid visa.
I.e, that you have a valid visa is a fact which the speaker acknowledges and cannot deny,
though the speaker says that that doesn't matter.
Even if you are in possession of a valid visa, by contrast, presupposes nothing about your visa.
You may or may not have a valid visa, and the speaker says that that doesn't matter.
They are both accurate, but they have potentially different meanings.
1) Using the one with although indicates, in the example given, that the person concerned is indeed in possession of a valid visa. But 'although' they have a visa they will not necessarily be able to cross.
2) The second using even if can also be substituted in the above case, but it can also be used where the person concerned does NOT have a valid visa. Indeed someone might say 'It is not certain you will be able to cross because you don't have a visa, and even if you had you might be prevented from crossing'.
Both indicate that a valid visa is not a sufficient condition for being permitted across the border. The one with although assumes that the addressee indeed has a valid visa. The one with even if allows for that as a possibility but does not assume it.
