Bad genie, that's a bad g'damn genie!! First, you have to assess the
victim's lamp polisher's needs. He may want the Ferrari, but if he has to haul his boat (that was going to be the second wish) over the dirt road to the lake, he needs the Land Rover.
The 70-200 II is a great general purpose zoom, excellent for portraits, sports, etc. Perhaps less good as a travel lens. Also consider...do you need the extra 100mm?
What body? Personally, I found the 70-200 II to be an awkward focal length on APS-C - too long indoors, often not long enough outside. On APS-C, the 70-300 L may be better for the reach. On FF, 70-200 is a great range.
One mor thing...if the genie can deliver the 70-200 II, he could also deliver the 70-300 L and $750 for something else...17-40L, 50/1.4 + 85/1.8, 600EX-RT, etc.