Well, for one thing, if congress itself or it's members are attacked, they are very likely to declare war with an unspecified enemy. Such a declaration would immediately transfer full authority of the armed forces to the president (to be used freely outside of and inside U.S. territory), and this until a peace treaty is signed. Furthermore, if an attack is in progress, this declaration does not require a majority vote, the president merely needs to find (what he reasonably believes to be) the highest ranking member.
So one (probable) difference would have been that president Bush would not have asked Congress what to do if Congress was directly attacked. He would have simply decided what to do and done it, after having received the declaration from Nancy Pelosi.
This would have lead to the combination of having a single deciding vote of what to do with the armed forces at the command of a single politician, making for easy and quick decisions and the entire country clamoring for revenge.
I'm not saying it would necessarily have lead to immediate counterattack, but it certainly wouldn't have lowered the odds of that happening.
After 9/11 - on 12 September 2001 - NATO invoked 'Article 5', the mutual self defence clause. This was on a provisional basis subject to evidence being provided that the bloke in a cave on a dialysis machine (or whatever) was guilty. However, the use of 'Article 5' meant that every member of the NATO alliance had the go-ahead for war without a single member of congress or member of the UK parliament having to vote on matters.
Congress and the British parliament were asked to vote for the war, this was not because their support was needed for the war to go ahead, had they all voted 'no' then that would not have trumped the 'let's kill' NATO card.
The Secretary General of NATO had a role in starting The War Against Terror, at the time the person in this role was one of Tony Blair's mates (his former Defence Secretary) and he was not American or voted into office by 'the peoples of NATO'.
