Ryan explained the economic plan better than Romney did - force Congress' hand, something the current administration has failed to do, repeatedly, even when their party had control of Congress. The general idea is to do pretty much what Reagan did in the 80s - say, flatly, we're dropping taxes by x, make up for it with cuts and the closure of loopholes. Everything is on the table except for military spending, apparently, which means there's a large pie to pick from.
Then again, the only place they're going to get any real money from is social security and medicare, but apparently they're kind've-sort've-off the table. The Republican ticket can't possibly revoke benefits to those already seeing them so, in essence, they can only remove benefits for people under 50-ish.
The "goal" with the tax cut is to promote small businesses who regularly make 250k or more in a year of profit. For fear of the massive corporate taxes in America, these people elect to claim it all as personal income, instead. The problem is that this plan doesn't actually address the problem - the corporate tax rates - and the only people who were talking about it before were Jon Huntsman, who was quickly neutered, and Rick Santorum, who was bat-shit crazy.
The tax cuts are really benefiting venture capitalists, which is good, and the extreme wealthy, which is not so good. You want venture capitalists to have more money to invest in more small businesses to make more money. You don't really want Paris Hilton to have more money, but it's a side effect of the drug. Whether or not the side effect is worse than the illness is up for debate. Personally, I'd rather most VCs have money and Paris buy a new bag than Paris buying that bag while the VCs buckle down.
Obama's plan has not, will not, and can not work in America. The federal government can not provide long-lasting jobs en masse. Most of his favorable job statistics come from temporary work, specifically in construction, that lasted less than 6 months. The whole notion that the fed can come in, buy up businesses, and put them back on their feet is a little off. The only American car manufacturer that is doing very well right now is Ford - and they didn't want the money in the first place. Remember, Ford was forced to take the loan.
GM is still not "out of the water" and though their sales have increased slightly, that's more to do with the plans they had before the bailout actually working now. The licensing of Fiat, the rerelease of the Camaro, bringing back the Challenger and the Dart, etc. All of these things are things that the car community has known about for years - the Camaro and Challenger, respectively, for at least a decade.
What about the other companies? More busts than not. Let's not even talk about the green jobs he was going to create with the fed that died out.
Basically, they're both wrong for different reasons and, IMHO, Obama is more wrong than Romney - just not by much. If you want jobs created, you have to let the people with the money to create them see profit in it. The only way the government can honestly promote permanent job growth is through tax cuts - they're just planning on cutting the wrong taxes.