Being asked to compare the Horseshoe to the Big House is like having to pick between a Corvette and a Mustang: Either way, you're going to be happy with what you get. In saying that, however, the answer to this question is really quite simple. When push comes to shove, the Big House really can't hold a candle to all the Horseshoe offers.
Although Michigan Stadium has a maximum capacity slightly larger than Ohio State's (107,501 to 101,568; although most game attendances exceed those numbers), the number of fans at the game are irrelevant unless they make some noise. After Ohio State defeated Iowa in 1985, Iowa head coach Hayden Frye complained that the crowd was too loud to call plays, and he actually attempted to create a rule which penalized teams for having too loud of crowds. This all goes without saying that all of this happened before the major renovations of 1999-2000, and the stadium could only hold roughly 90,000 people at the time.
For other examples of Ohio State's stadium noise overwhelming the opposition, look no further than Michigan's current starting quarterback, Chad Henne. In 2004, Henne was enjoying great success as a freshman, leading his team to an eventual Rose Bowl berth against Texas. The majority of the country, including Henne himself, expected to cruise to victory over a struggling 7-4 Ohio State team. The game ended up being Henne's worst of the season, and afterwards he openly admitted to the atmosphere at Ohio State being much more than anything he had previously anticipated or experienced.
Another factor playing a role in the superiority of Ohio Stadium is all of the tradition that is associated with it. Perhaps the most time honored tradition in not just college football, but in all of sports, Script Ohio, has been played at every home game ever since it's inception in 1936. The dotting of the "i" has been ranked as the #1 tradition in college football by Athlon Sports. Script Ohio is much more than just simply a marching routine; it is a tradition that gives the university an identity. Only six non-sousaphonists have ever dotted the I, the most recent coming this season against Michigan when the most famous non-football athlete in Buckeye history, Jack Nicklaus, had the honor. The rest of the traditions that are synonymous with the Horseshoe -- Carmen Ohio, Hang On Sloopy, etc. -- are second to none at the collegiate level.
Having been to Ohio Stadium a couple times, I feel uniquely qualified to answer this question. Unlike a shady politician (no doubt from Ohio) who would answer such a query without all the facts, I can speak from firsthand experience gleaned from my trips to Columbus (surprising as it may be for some to believe I got out alive and thus live to tell about it).
Michigan Stadium is better known as The Big House, which is appropriate seeing as its the largest college football stadium in America. It's not "A" Big House or "One" Big House or even "Some" Big House. No, it's simply The Big House implying there is no other. And of all people, Buckeye fans should understand the significance and definitive nature of the word "The" before a name or title.
Ohio Stadium on the other hand is often referred to as The Horseshoe, or simply The 'Shoe. However, since the stadium renovations a few years ago which made the seats in the once-open end of the stadium permanent, it really doesn't look much like a horseshoe anymore, does it? Then again, I guess calling it the "U With A Line Across The Opening Part" doesn't really roll off the tongue.
The incredible thing about The Big House is that upon first approaching, it doesn't seem like much. Hell, it's not that tall, that "big"...until one walks through the tunnel and first glimpses "the hole that Yost dug, Crisler paid for, Canham carpeted and Schembechler filled each and every Saturday" according to legendary U-M announcer Bob Ufer. It's truly breathtaking. A sea of 110,000 maize and blue faithful cheering the Wolverines on.
Best of all, there's not a bad seat in the place. Because the stadium was literally carved out of the ground, there are no support columns or poles to obstruct one's view.
As for the "U With A Line Across The Opening Part," one is immediately struck by the fact that they have state troopers standing atop the brick towers at one end of the stadium. Each time I see them, I'm reminded of prison guards (and this was long before Maurice Clarett). I guess their purpose is to help spot fires around the campus during the famed Burning of the Couches after a big Buckeye victory...or loss...or any random Thursday night.
Furthermore, in addition to large support beams in the stadium, one's view in the 'Shoe is also often obstructed by the large Ohioans.
While Michigan plays on comfortable, sure-footed synthetic Field Turf, Ohio State plays on natural grass...when it's not just a big clump of dirt...or being replaced for the 36th time this season.
In a nod to our great country's democratic roots, in which all football fans are created equal, Michigan Stadium has bleacher style seating, all the exact same size. This is simply the university's way of not playing favorites with Wolverine supporters, making no distinction between rich or poor, large or small, as all the maize and blue faithful sit in identical seats, each enjoying the game in equal comfort (as long as nobody in your section weighs more than Nicole Ritchie).
Ohio Stadium on the other hand has many different sizes, styles and types of seats. From the high-priced luxury boxes where Buckeye boosters can cheer on the athletes they've chosen to support financially each football season to the crappier seats in the low corner of the closed side of the stadium where they stick the Michigan fans, giving those higher up a perfect target to hurl obscenities and other more tangible objects.
As for which stadium has the best seats, I believe in the equality that America was founded on (and the U-M athletic department's assumption that no human being weighs over 132 pounds). Thus...
Ok, here is one category where I must give the nod to our Buckeye brethren to the south. Sitting inside the 'Shoe during a game is something akin to sticking one's head in a jet engine. When not hurling F-bombs at frightened Michigan fans or spelling other four-letter words such as O-H-I-O with the rest of the stadium like they're practicing for a really easy spelling bee, OSU fans can be a loud, intimidating bunch that turn The Horseshoe into one of the loudest stadiums in all the land.
Michigan Stadium...not so much.
Michigan fans are very fond of the "key play" cheer by which, during "key" moments of the game like a critical third down for the opposing team, U-M fans -- in unison mind you -- reach into their pockets or purses, withdraw their key chains...and begin to jangle them with all their might. The hope here is that the mere sight of tens of thousands of Wolverine fans shaking their car key against their house key -- over and over again in the stadium -- is enough to cause an illegal procedure penalty for the opponent, either when the sun hits the keys just right and blinds them or from laughing so hard at the lameness of it.
Advantage: Ohio State
As you can tell by my scientific analysis above, it's obvious "The Big House" is infinitely better than the ol' stinky 'Shoe.