I never understood why people referred to the PS360 as HD Twins.
They were called the HD twins because outside of minor differences, they were pretty much the same. One was a little more powerful, one was a little cheaper, each got a handful of their own exclusives (not counting first-party), and their markets were pretty much identical (with FPSes pretty much dominating).
The only real differences were that the PS3 had a stronger Japanese presence, whereas the Xbox 360 had a stronger American presence, in terms of support, and that their later motion control systems worked differently from each other.
What sets the Wii U apart, other than first-party things, is that it has unique controls as standard - this practically guarantees a variety of exclusive titles from most third parties.