Most of the post-convention coverage was about how much more excited the Democrats were than the Republicans. By this measure (getting the press excited) the Democrats won, hands-down. Since the press do not elect the president, no matter how much they try, we have to look at other measures.
Keep in mind that the conventions were aimed at different demographics. The Democrats wanted to rev up their base. They need a big turn-out from youth and minority voters in order to win. These groups turned out in record numbers in 2008 but show every sign of dropping back to indifferent participation numbers.
The Republicans were trying to attract undecided moderates. Romney spent the primary season courting the party base. If they are not excited about him, they are at least resigned and excited about beating Obama. Romney needs the swing voters to win.
The Democrats had a red-meat convention. They trotted out activists, mayors and ex-presidents. They were also in a smaller hall which amplified cheers.
The Republicans trotted out rising party superstars. Regardless of who wins this election, the next Republican candidate probably got prime-time exposure at this convention. The Republicans had an orderly convention. They always have an orderly convention. The last time there was any real excitement at a Republican convention was in 1976 when what was to be a short demonstration in favor of Reagan after he was nominated lasted 20 minutes.
Both Romneys gave good speeches. Ryan gave a good speech. His was so good that partisan fact-checkers pounced, elevating quibbles to lies. Clint Eastwood stole the show and gave what is still the most talked-about speech of either convention.
By most accounts, Obama gave the 3rd best speech of his convention (a minority put him 4th after Biden). Michelle got top marks and Clinton came in second. A close examination of Clinton's speech shows that he seems to be unaware that Obama is running against his economy as much as Bush's. There are also places where Clinton praises Obama for traits that he does not ahve but Clinton did (cooperation with the other side).
The Republicans had to deal with the threat of a hurricane but otherwise the convention went smoothly.
The Democrats had several unforced errors. A fight over the party platform turned ugly and reminded the public about how far the Democrats have moved to the left. Obama was originally going to present his acceptance speech in a stadium with extra seating to accommodate the 80,000 that he had four years ago. At the last minute the speech was moved to the convention hall. The stated reason was the threat of rain. There was speculation that the real reason was that they could not fill the stadium.
The real measure of a convention was how much they helped their candidate. To evaluate this, I looked at Rasmussen. Unlike other polls (see above about the press electing the president) Rasmussen has a good record of identifying likely voters and not over-sampling Democrats. He showed each candidate getting a post-convention boost. Romney took the lead for a few days from the end of the Republican convention until part-way into the Democratic convention. Obama took the lead after Clinton's speech and held it for a few days.
Now that the conventions are over, neither candidate has a lasting bump but Romney seems to have made the most gains. Before the conventions he was down by four. By today he was ahead but only by one point.
This is bad news for Obama. Neither candidate is polling over 50%. Traditionally the undecided voters break for the challenger. They have had four years to get to know the incumbent. If they have not decided for him by now they never will.
Two things will still affect the election and neither favors Obama. One is the debates. Obama was a mediocre debater in 2008 and he has not debated since then. He personally detests Romney which might make him prone to gaffes. Romney held his own or won against such intellectuals as Gingrich. He has a strong opertunity here.
The other factor is external events. The economy is hurting Obama. Stories about stimulus money being wasted are beginning to come out. Multiple countries are having violent protests against the US with four US citizens already dead. Romney is able to stand to the side and snipe which is why the reaction was so strong to reasonable statements about the attacks on two embassies.
So, coming out of the conventions, neither candidate gained a clear advantage so we are in for a long, nasty campaign.