This depends on context. While I don't believe there is a perfect single word for this, this is certainly a common and generally recognized concept. Most famously, A Tale of Two Cities:
It was the best of times, it was the worst of times,
it was the age of wisdom, it was the age of foolishness,
it was the epoch of belief, it was the epoch of incredulity,
it was the season of Light, it was the season of Darkness,
it was the spring of hope, it was the winter of despair,
we had everything before us, we had nothing before us,
we were all going direct to Heaven, we were all going direct the other way
The above quote is describing the same thing as a multitude of contradictory (to the point of being exact opposite) statements. The author of the book put the thing in juxtaposition with itself. Usually, one would juxtapose two (or more) different things beside each other to compare/contrast them, but in this case the author is doing a self-juxtaposition.
If your context is the same as the quote, one could describe the thing as being in a state of superposition, referring to a state of Quantum Superposition wherein a thing is both states of a binary relationship (both alive and dead) at the same time.
In math, namely geometry, to describe things that are almost the same but not exact, you would say they are similar but not congruent (a 5in. x 5in. square is similar to a 6in. x 6in. square, but not congruent).
A common proverb you could use to describe them could be different sides of the same coin, meaning that both parties are the same thing, just from a different angle.
And I feel that an oxymoron comes close to matching with your description, but doesn't quite get there.
Since there unfortunately isn't a perfect single word for this phenomena I would think the best way to go about describing it would be to explain it in a few words:
"The brothers were arbitrarily either on the same or different side of the same coin: sometimes they seemed like the same person, at other times they didn’t even seem like brothers."
"The brother's personalities were in a state of superposition: sometimes they seemed like the same person, at other times they didn’t even seem like brothers."
Personally, as a phrase, I like "same, yet opposite."
"The brother's were the same, yet opposite: sometimes they seemed like the same person, at other times they didn’t even seem like brothers."