Difference between "evade X" and "sidestep X"?

Solution 1:

I would consider sidestepped the slightly more informal of the two words. That said, I like it better than evaded in this context.

With evade, I often think of eluding capture, like a criminal evading the authorities. That's not the only meaning of the word, but it is one of them. In the context of a press conference, I'd think that one who evaded questions on certain topic might abruptly announce the press conference was over, and walk out of the room. Someone who sidestepped the questions, though, would remain at the podium, and avoid answering the questions directly - this is what I assume the writer is trying to describe.

Solution 2:

In these sentences, they mean the same thing. Side-step is one technique for evading. However, since they are both being used in the figurative sense, they have virtually identical meanings in this context.

If they were used in describing an actual fight

The boxer side-stepped the blow from his opponent

would be a more specific version of

The boxer evaded the blow from his opponent

because if you simply say "evaded" he could have ducked, stepped back out of range, etc.