Two slightly different dimensions. Some places have higher status faculty whose letters and connections might get you further, but who are less willing to collaborate with grad students and so might leave you less likely to become a high quality researcher. Ideally, you want to be well trained and well connected -- visit days should help you figure out where schools are on the tradeoff frontier.
I will also say on reputation -- from the outside it is tempting to take e.g. 15 year old flyout rankings etc. as gospel because they do a lot of the thinking for you. Most faculty I talk to have a much fuzzier and heuristic approach to ranking schools, and they know much (MUCH) more about the quirks of individual programs (i.e. X high-rank program is incredible for training in Y field, but their students doing Z are worse off than those at Q). You should talk to faculty to get a sense of these types of things, I think.
As others have alluded to though, personality and place are also important parts of fit. Five to six years of an instituion being among the most important things in your life -- make sure you get along with the grad students and enjoy the location! Remember, it's a TWO sided matching problem!
