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Which test is prefered does indeed depend on the school. For instance, to the best of my understanding, you can get by with having given just the GRE and not the GMAT though the reverse may not be true. Re: the importance of verbal vs. quant, I would say that quant is infinitely more important than verbal. I mean it does not hurt to have a 700+ on your verbal (I am talking GRE here), but if it is not matched up with a 780 or higher on the quant, then it doesn't matter. I remember having seen the profile of someone on the PhD Econ forum who got into Stanford GSB's Economic Analysis & Policy and Harvard's Business Economics programs, arguably the most competitive in all of B-school, with a 380 or something on the verbal. Needless to say everything else on the profile was great. However it would have been all but impossible for someone to get into a school of that calibre with less than a 90 percentile or so on the quant section.
Work experience is absolutely unimportant for getting into a PhD. Frankly there are some schools who look at work ex as a distraction. What many candidates at top schools have however are graduate degrees in related disciplines, e.g. if they are in a OB program, they may have had a MS in Sociology or Psychology, if they are in an Econ program, they may have a MS in Econ/ Math. Nevertheless there are a large number of students who come straight out of undergrad as well. In fact, my only other colleague in the Business Economics program at a top 10 school is coming straight out of her undergrad.
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