Admiral346:
411, the PHX tracon might want you to fly the original missed.
But do not assume that this is a rule valid on all sidesteps everywhere!
At my base in MUC the RWYs are very far apart, and miss takes you either 90deg north or 90 deg south, depending on the RWY.
Now if you flew the miss to the N from the southern RWY, it would be very dangerous. You usually get the sidestep, because they have lots of departures waiting at the original RWY, and low traffic on the other one.
I've never been to MUC, but based on the Jepp charts none of the ILS approaches at MUC have side-step minimums, nor do they have circle to land (CTL) minimums. So, if ATC clears you to "sidestep" to the parallel runway that sounds like it would be a visual approach.
As to the United States, 411 is absolutely right, as is the PHX TRACON controller. LAX does not have CTL minimums but it does have sidestep minimums to the adjacent, closely spaced parallel runway. The clearance, "Cleared for the ILS 24R, sidestep to land 24L" is nonetheless a clearance for the 24R ILS.