One is that Rice -- despite promoting a vision of what she called "unity of purpose and message" with Europe -- announced no changes in policy in areas where fundamental difference still exist between the United States and the European Union.
The other is the belief that Bush himself is the only figure who can speak with authority on potential changes in U.S. policy.
As a result, eyes in Europe are already looking ahead to Bush's visit to EU and NATO headquarters on 22 February.
Fraser Cameron, director of studies at the Brussels-based European Policy Centre think tank, tells RFE/RL that while Rice's visit showed a change in style, it did not deliver a different message.
“There is no breakthrough yet. There is a change in rhetoric, a change in style, a change in tone, but not yet any change in substance," Cameron says. "I think the European Union will be looking, when George W. Bush comes, for a change in some major policy areas -- principally, engagement in the Middle East; secondly, the willingness to at least engage in discussion on climate change; and also to support multilateral institutions. These are just three key areas for the European Union.”
Cameron stresses that it was n-o-t the purpose of Rice's visit to announce any substantive changes. Instead, he says, Rice came simply to signal the willingness of the second Bush administration to engage with Europe.
Another analyst, Michael Emerson of the Centre for European Policy Studies, agrees. He tells RFE/RL that Rice’s visit was about what he called "restoring good atmosphere" -- but nothing more.
“I think it was a significant and successful diplomatic event -- in the best sense of the word diplomatic -- no more and no less,” Emerson says.
The secretary of state, Emerson adds, presented herself as an attractive partner for Europe, aided by her academic background and a reputation for being well-informed.
If a full breakthrough in U.S.-EU ties in not yet in the offing, Emerson says, then at least the time has come for a new phase -- as recent developments in Iraq and the Middle East demonstrate.
“A break is perhaps slightly strong language, but certainly a new phase is there. Because in addition to the fact that, as I’ve already mentioned, [Bush's second term] is coinciding with a new Middle East, a new Iraq -- in addition to all of that, Washington and certainly Condi Rice are fully aware that the U.S. international diplomatic reputation had sunk to the lowest level possibly ever,” he says.
Emerson cautions, however, that Rice’s diplomacy and Bush’s own vision are two different things -- although the new secretary of state is not without influence in the presidential administration.
“From a European point of view, I think Bush is still regarded as a hopeless case, if you want to really talk about the Bush vision [that] you would get talking one-on-one with the president himself," Emerson says. "But the administration is a complex thing, and [Bush] has important colleagues, and Condi Rice is one of those important colleagues.”
Cameron also notes in an article released today that Bush faces an uphill battle if he is sincerely seeking to improve relations with Europe. Cameron writes: "The vast majority of Europeans still view Bush with a mix of suspicion and disdain.”
Both Emerson and Cameron identify two potential major stumbling blocks for EU-U.S. relations. One is the EU's plan to lift its arms embargo against China. The other is Iran and how best to deter its alleged pursuit of nuclear weapons.
Cameron says the EU has not done enough to address American concerns about China.
“I think Europe as a whole has underestimated the significance of lifting the arms embargo to China on both the United States and other allies, including Japan," he says. "I think the issue needs to be worked through more with the United States administration and with Congress. There was a very large majority when there was a vote on this in Congress a couple of weeks ago -- against the European approach."
He says the EU could make the arrangement easier for the U.S. to swallow if it managed to extract concessions from Beijing on human rights. And he says it is crucial for the EU to ensure the lifting of the embargo does n-o-t lead to increased arms sales to China.
Emerson thinks Iran may pose an even more difficult problem for the EU. He notes that in Washington, there are what he calls “extreme divergences of opinion," and adds that Rice herself has studiously avoided ruling out an attack.
The next few months, he says, are crucial.
“That is a question, as to what happens between now and, say, the month of June," Emerson says. "First, whether the European negotiation process aborts or progresses. And then, secondly, how the Americans play it -- coming in behind and in support of the Europeans, or standing apart from the Europeans waiting for the Europeans to fail? And then for some -- maybe in the Pentagon or the 'neocon' hawks -- [whether] to bomb all the nuclear establishments in Iran or to let the Israelis do it.”
Cameron also stresses there are strong voices in Washington calling for regime change in Iran. Meanwhile, he notes, most EU leaders -- including Tony Blair of Britain -- have made clear they regard the military option as “unthinkable.”