"It's a half an inch of water, and you think you're going to drown."
One of the key criteria for AAU membership is "competitive" research dollars. A large chunk of federally sponsored Ag research is non peer reviewed and thus does count toward this AAU membership criteria. Not surprisingly, a decent chunk of Nebraska's research is non peer-reviewed and this was a key factor in their lack of support from its AAU brethren.
The AAU then adds a double whammy by also looking at the competitive research dollars per faculty member. However they don't exclude Ag faculty members from this calculation. Meanwhile non-tenure track medical school faculty (for which Medical Schools rely upon heavily for research) are not included in this calculation.
These criteria clearly put land-grant universities trying to gain membership (or those current members in the bottom quintile) -- especially those without significant medical school research -- at a disadvantage over private schools and public institutions that do not have such an agricultural mission as one of their mandates.
While research funding certainly is an issue with the AAU vis a vis Tech, a potentially bigger issue is the PhD programs at Tech. They tend to be overwhelmingly concentrated in a few distinct areas (mostly STEM). While that's not necessarily a problem for certain high power STEM-focused schools (Cal Tech, MIT, GIT), VT considers itself a comprehensive university. The lack of a comprehensive research program is problematic.
I'll point out that one of the most recent three schools to gain membership was a land-grant with a strong ag focus -- A&M. It's also a much more comprehensive institution doctorally than is VT (as is the other school to gain membership in '01 -- SUNY Stony Brook).
Federal research money is distributed on merit. All federal grants are awarded through peer review. You create a proposal which is then vetted and graded by reviewers (academics, for the most part). The proposals are graded on potential for advancement of knowledge, potential impact on society/field, and the quality of the research team/facility.
Now, that's where some subjectivity enters the process -- reviewers are interested in who the Principal Investigators (PIs) are, where they went to school, what they've published, and what grants they've had before. A researcher who trained at a top school, had pubs from her graduate school period, did a post-doc at a top facility, and has good connections will probably get the benefit of a doubt that a less well-connected researcher would not enjoy. PIs who get grants in the past tend to get grants in the future because they're known commodities. This is why there's such emphasis on top schools attracting top faculty -- it's the faculty (the PIs) who get the grants, not the schools. The schools take a cut (more on that in a bit), but the PIs are the ones who win the grant and are held responsible for the outcome.
Some schools are better at attracting grants than are others. When we were in College Station, my wife worked for TAMRF (Texas A&M Research Foundation, a non-profit affiliated with A&M whose sole function was to help attract grants and then administer them once awarded). Most large doctoral research universities do this, but (like anything) some are better at it than others. TAMRF was very proactive, especially with graduate students and non-STEM fields. They knew they could get STEM grants fairly easily, but they also wanted to get as much grant money as possible.
Grant-writing is a skill, as is grant administration. Some are better at it than others are, and some are willing to do more to attract these folks to their staffs. Screw up the proposal or the administration of the grant, and the feds probably won't do much business with you. Writing a grant proposal is not easy, nor is administering it. It's like any other federal contract --lots of regulations, generally imposed to ensure the taxpayers' money is spent as promised. My wife's sole function was to oversee subcontracts from TAMU grants to overseas researchers who were part of grants awarded to A&M PIs and to ensure that the funds and reporting complied with federal regulations. If you were a Clemson faculty member subcontracted to a TAMU grant, somebody else in TAMRF oversaw the subcontract.
A top graduate program also helps attract grants. Grad students and post-docs are the ones who usually do most of the grunt work on the grants -- if you don't have quality grad students (and can't attract them), then an institution or PI probably won't get too many grants. Schools have an incentive to encourage grants -- they charge an overhead cost to PIs to cover administrative and other costs. Since grant budgets usually include equipment costs, the schools generally benefit there as well.
If you want more grant money to go to a specific school, you have to be willing to do certain things. You have to be attractive to top faculty and top graduate students -- not just in terms of geographic location and in resources, but in other intangible quality of life issues. You have to have programs that attract top students and faculty -- and be willing to devote the resources to those programs. You to create the infrastructure to facilitate grants (i.e., research administrators, grant-writers, and the like -- see TAMRF). Some schools are better at this than others. But the grants are, in the end, awarded on the merit of the proposal and the PI.
Yes, your tax dollars are going to UCLA ... and will continue to do so. Just as TV networks know the national audience is there for ND, Michigan, UF, and USC and not there so much for UAB and WVU, so too do reviewers recognize UCLA is a known commodity. If you want to move up, you need to be willing to do what it takes to lure the researchers away from UCLA and the like. And that's more involved than just hiring the hot new PhD in a specific field. Some states are willing to spend more on public research universities than others are (just like some schools are more willing to spend on athletics than are others). As long as that's the case, expect those states (and those schools) to garner more of the grant money. Some recruits prefer cities to rural towns; same with faculty and grad students.