The last big Battlefield was BF4, which came out in 2013 against Ghosts, one of the worst selling, worst received CODs ever made. Battlefield 4 sold 7 million units as of May 2014. As of February 2014 (several months earlier than BF4's sales report), Ghosts sold 19 million units. That's a huge difference. According to NPD Group, BF4 was the second best selling game in November of 2013 in the US. Guess what number one was? It was Ghosts.
Here, let me do you the courtesy of running through each game individually. You can fact check me later, but I did my research. Let's start with Bad Company 2, because BC1's sales aren't available from what I can find.
Bad Company 2 was in competition with both MW2 and BO1 due to its release time in early 2010. MW2's was over $1 billion as of January 2010. That's just a couple months after launch. Your "it sells more over its lifetime" claim is false for each of these. Black Ops 1 beat MW2, selling over $1 billion by December. Both games launched in November. Within the same period of time (roughly two months), Bad Company 2 sold over 5 million units by May of 2010, after being launched in March. It took until March 2012 (2 years later) to reach 12 million units sold.
While obviously it's not this simple, we can estimate (give or take a few million due to price drops, currency rates, special editions, etc.) that BC2 sold roughly $720 million. This is very heavily estimated due to those variables I mentioned. I got this number by multiplying 12 by 60 (average price of a game in US, since this is all in US currency). Took two years to get to that point, still not higher than MW2 or BO1 individually.
The next are less complex, I promise.
BF3 sold 15 million units by June 2012, roughly 8 months after launch. Numbers don't go past 16 days after release for Modern Warfare 3 which came out the same year, but they don't need to. Only 16 days after launch, MW3 sold over $1 billion. Using the same rough conversion of units sold*60, we can see that BF3 sold about $900 million in 8 months. MW3 beat that in 16 days.
BO2 sold over $1 billion in 15 days, beating MW3's 16.
In 2013, BF4 and Ghosts came out. Already did the math above.
Hardline came out in early 2015, competing with Advanced Warfare, mostly. EA did not release sales numbers for Hardline as far as I can find, probably because they weren't anything special. Just to get them out there, however, Advanced Warfare sold 27% less than Ghosts in November. Both games did poorly, critically and commercially, but judging purely by trend, it's not hard to imagine AW still sold more in its lifetime. That's purely speculation, though.
Last up, while not an official Battlefield game, Battlefront functionally served as EA's big shooter release of last year, like Battlefield typically does. Battlefront sold roughly 13 million units as of January of this year. BO3, however, sold significantly better than the last two CoDs, selling over $550 million units in just 3 days (roughly 9 million units, but that's only in three days). It was the best selling game of last year, too, meaning that it definitely beat Battlefront and Battlefield Hardline.
One last fact: CoD has been the highest selling game every year one has been released since 2009 with the exception of 2013, where it lost to GTA V, but came still came in second place (so it beat BF4).
Your statements are factually wrong. None of this means CoD is better or worse than Battlefield. In fact, I am not a massive fan of either franchise, I just think factuality and accuracy is very important. You, or the person I initially responded to, or anyone else shouldn't make claims like that unless you can back them up with fact. This has not been an exercise in fanboy-ism, rather, it's been one in the importance of factuality and accuracy, as I stated. I do not have a dog in this fight, I do not care which game sold more or less, I care about facts.