I ask that you please do no base your opinion on videos of an institution. The goal of marketing media is to largely attract individuals. Therefore, they only show 5% of an institution. I recommend visiting both schools and speaking with alumni.
The Citadel and VMI are excellent schools to prepare young men and women for commissions in our nations military or civilian professions. Like most any institutions of higher learning, The Citadel and VMI are not perfect. Nonetheless, I believe they will prepare you much more effectively in leadership and ethical training than civilian schools with ROTC programs.
The Citadel and VMI both offer commissions in The Air Force, Army, and Navy. VMI has produced top 10 ranking nationwide ARMY ROTC cadets. Likewise, The Citadel's Army Cadet Battalion was ranked number 1 in its region a year or so ago. Speaking with civilian ROTC cadets who've participated in Marine OCS, they can validate that VMI and Citadel cadets have fared exceptionally well during the program. Prior Enlisted individuals who've earned commissions through the STA Program at The Citadel have outperformed their peers. (The #2 ranking Navy SWO in the nation this year was a Citadel graduate prior enlisted, as were two others who were in the top 10)
With regards to academics, both institutions offer a rigorous core curriculum. While their core courses are not technical in nature to their service academy counterparts, Citadel and VMI's engineering programs have earned national accolades. Both The Citadel and VMI were tied for #21 in top undergraduate engineering programs where doctorates are not offered (USNEWS 2012).
VMI was ranked #70 in National Liberal Arts Schools, and The Citadel was ranked number #1 in Southern Public Colleges which offer up to a masters degree. For Forbes ranking VMI was #115 and The Citadel was in the 300's.
For postgraduate fellowships, VMI has produced numerous Rhodes, Marshall, Gates Cambridge, and Truman Scholars, Whereas the Citadel is mostly a Fulbright granting institution (23 winners) with Truman winners.
The Citadel in terms of demographics offers the beautiful Charleston SC (one of the top 10 most beautiful cities in America), While VMI in Lexington VA is more rural.
If you want to factor alumni success through awards and ranks then it can be compiled as follows:
The Citadel has produced four Navy Blue Angels (including the current cmdr), six governors, three US senators, one astronaut, and 1 four star general and 27 three-star generals, three or four current NFL players. Many CEO's
VMI has produced 7 four-star Generals including 1 five-star (1 Army Chief of Staff, 1 Air Force Chief of Staff, 2 Marine Corps Commandants), 1 Nobel Prize Winner+Secretary of State (Gen. Marshall), Four Medal of Honor Recipients, Many CEO's
Both institutions have a rich history dating back to The Civil War and have countless alumni who have sacrificed their lives for our country. Both have strong alumni communities.
The Citadel has both an undergraduate corps of cadets and also a civilian graduate program, VMI is solely comprised of an undergraduate corps.
I honestly believe both are fine schools. What determines your future as a competent officer or business leader is largely driven by the opportunities and legacies you take and leave as an undergraduate. You can spend four years doing the bare minimum and leave with a sense of regret, or you can become a top ranking army cadet, Rhodes Scholar, and Regimental Commander/First Captain. The choice and path is ultimately up to you. Seize The Day.