I don't like to compare schools on measures like "academics" — there are just too many moving parts. I think it's tempting to say we know The Rankings, as if there are any rankings in the first place that mean anything at all, or any meaningful distinction between, say, Yale and Stanford that can be measured and assigned a number. The more I've learned, the more I've realized that most students can be happy at many different schools. More important: the more resilient the child, the more likely his or her school career will be positive. In the history of DC schools, no child ever got a crappy education because she went to WIS instead of another DC school.
As for whether WIS might fit your family: The school, as others have noted, has something of a monopoly on the IB program (insofar as anybody can apply — my own child is about to complete an IB program but it's a public school, so it's only open to students in our boundary). If that kind of learning appeals to your family, WIS is a great option and provides more opportunities than any student can take advantage of, as well as unmatched international diversity. If you want an IB curriculum, you like your tour, and your children are fortunate enough to have the family means to attend independent school, I wouldn't hesitate for a moment to apply.
Peter
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Disclaimer: The anonymity here makes me uncomfortable; it's easy to be uninformed, personal, or simply mean-spirited if people don't identify themselves. For that reason, I have an account so you know whose words you're reading. I have more than 20 years' experience as a teacher and administrator in independent schools, and I have counseled hundreds of students in finding their next schools. I hope I can be helpful to some folks. If you don't like something I've said, you're in good company — there's a long line of past students and parents ahead of you.

If you want to chat further, please feel free to contact me offline: peter <at> arcpd <dot> com