First, remove all consideration of movie reviews. Early reviews for Civil War seem positive, but Winter Soldier still sits at 89% on Rotten Tomatoes and was a bit north of 90% when it opened to only $95M. Reviews will impact word of mouth and the legs of the movie, but probably have little impact on opening weekend where fans have already decided they will see the movie or avoid the crowds the first few days.
Marvel has established itself as a powerful brand in the movie market (the Marvel Cinematic Universe or MCU). So there's a lot of comparables at http://www.boxofficemojo.com/franchises/chart/?id=avengers.htm
Factors in favor of Civil War opening > $166M:
* More characters generally = more money. Avengers opened to $207 (highest in MCU), Avengers 2 opened to $191 (2nd highest), and even Guardians of the Galaxy opened to $94M (7th highest but impressive given the August release and low name recognition of the characters prior to the film).
* The MCU is the house that Tony Stark (or Robert Downey Jr) built. The five highest opening MCU films are the five with Tony Stark/RDJ: Avengers 1 & 2 and the three Iron Man films. While two of those movies opened under $166 they were the first two--Tony Stark's lowest opening weekend in three years is $174.
Factors against Civil War opening > $166M:
* Captain America. Despite both Captain America films being very positively reviewed, BOTH of the first two Captain America movies combined for opening weekends less than $166 ($65M and $95M).
* Trendlines not in Cap's favor. Cap's first movie opened at $65M. HIs second at $95M. That was a 46% improvement film over film. Iron Man saw 31% and 36% improvement film over film so that 46% is impressive but with the lower initial opening there was more headroom. That's still true given Winter Soldier's $95M opening. But Civil War would need to improve 75% over Winter Soldier's opening to beat BvS--a feat that hasn't been accomplished since The Dark Knight improved on its predecessor by 229%. Even X-Men: Days of Future Past only managed to beat First Class (also a low opener) by 64%.
Many are also comparing Civil War to the Avengers. The commercials and trailers certainly make a big deal of all the characters (especially Iron Man) and for good reason:
* Avengers opened to $207, Avengers 2 opened to $191. That was only a drop of 7%, which if Civil War is considered a third Avengers movie and has the same drop then it would exceed $177M.
* The $177M also assuming a similar drop which might not happen since Avengers 2 reviews were mixed while CIvil War reviews appear to be positive.
However, it's entirely possible that movie goers outside the core fan base won't view this as an Avengers movie because of the title and because of Captain America (who is dominant in the advertising but has never had the same huge success as Iron Man). And while there are many characters in this movie, several of them have been minimally used (Ant-Man, Falcon), at least one is new (Black Panther), and others set to appear haven't even been heavily featured in advertising despite previous appearances (Vision, Scarlet Witch).
One additional reason why movie goers may not consider this an Avengers film is the absence of Thor and Hulk. Not only was Hulk a recognizable name, but both of those characters created visual moments that made the scale of the Avengers films grander than other MCU movies. Instead we have a current action shot of a number of normal sized people jumping/running/flying at each other on an airport tarmac.
Ultimately, I think the chances of Civil War outgrossing BvS on opening weekend comes down to two scenarios:
State 1: Civil War is considered by the public to be Avengers 3.
State 2: Civil War is considered by the public to be another Captain America movie.
In State 1, it is highly likely a third Avengers movie could exceed $166M on opening weekend. The first two movies did so, even despite the second movie's mixed word of mouth. There is a generally favorable opinion of the MCU and Avengers which would also help its performance. I would predict there to be a .90 chance that a third Avengers film beats $166M on opening weekend.
In State 2, it is highly unlikely that a third Captain America movie exceeds $166M on opening weekend. Only one superhero movie has been able to improve that much for a sequel (Dark Knight) and Civil War does not have the same core reasons for Dark Knight's success (media sensation of Heath Ledger's performance and low previous film opening). Although the marketing efforts around Civil War want to equate the movie to Avengers, I think that ultimately falls short and is further indication that Marvel doesn't trust the opening power of Captain America alone. I would predict there to be a 0.15 chance that a third Captain America film exceeds $166M.
Now we have to look at the odds that the consuming public views the movie in either state. The marketing is pushing towards State 1 but the success of the MCU, and particularly its increasing use of multiple characters within a film, are likely to make State 2 more likely. I would predict that movie goers are 0.75 likely to view this as a Captain America movie.
Chances that Civil War outgrosses BvS would therefore be:
.90 State 1 success * .25 chance of State 1 + .15 State 2 success * .75 chance of State 2 = .3375 or 34%.
UPDATE: The opening foreign numbers are starting to come in and international movie-goers are showing a much stronger preference for this to be treated like an Avengers movie rather than a Captain America movie. That's a surprise given their failure to do so with Cap 2 but it had for fewer additional characters. So I am updating the percentage change of State 1 to be .90 given the huge difference between Cap 3 and Cap 2 opening weekends in foreign markets.
Additionally, if you compare the foreign openings of Cap 3 to Ultron you do see a slight decline (just as we saw a drop for Avengers 1 and 2). These are difficult to compare as some have slight drops (Australia had $12.3M for Ultron, $10.6 for Cap 3), some are large increases (South Korea had $23M for Ultron, $29M for Cap 3), and some are large drops (UK had $27.3M for Ultron, $20.5 for Cap 3). But given that a large drop would need to be consistent for a third Avengers movie, I am increasing the percentage of State 1 succeeding to .98. So the new numbers look like:
.98 State 1 success * .90 chance of State 1 + .15 State 2 success * .10 chance of State 2 = .897 or 90%
I have entered another prediction with these numbers but wanted to update here as well.