Also speaking of high school counselors thoughts on both universities:
Hopkins garners a high school counselor rating of 4.9 out of 5.0 - 2nd in the country after Harvard, and in line with Stanford and Yale amongst others, (rating from a national survey of high school counselors for US News to assess the undergraduate education afforded by each of these schools).
Rice garners a 4.5 FYI.
Source:
http://colleges.usnews.rankingsandreviews.com/best-colleges/jhu-2077/rankings
http://colleges.usnews.rankingsandreviews.com/best-colleges/rice-3604/rankings