Do you really think it's "free" and not figured into the MSR price of the card? Still... it probably comes out cheaper than what you'd pay for the game retail.
Yes it was free. I can clearly see on the invoice where they showed both Black Ops 4 and BFV/Anthem as $59.99 each but then two -$59.99 lines on the invoice zeroing it out. They did take $59.99 plus tax off one charge to make it it's own charge and the difference of the total I paid was the other charge. They do this so you can't just get the game for free and return all the stuff I think. The card (RTX 2070 XC Black Edition) was $499.99. It's actually gone up to $539.99 since I bought it, still with the BFV/Anthem gift promotion.
Hard choice, BF V is a work in progress and still having issues. Anthem hasn't even been released yet. Even if you're asking on a gameplay standpoint vs polish, content, or RTX support, it's really hard to say, especially since you said zero about gameplay preference.
This is true of most games regarding RTX support, because Nvidia released these GPU models on nothing but hype and a very misleading stage demo. It's worth noting though that Anthem still doesn't appear on any lists confirming RTX or even DLSS support. Since it uses the same engine but probably a different variant of it, that indicates only the devs know these details.
This is also why a lot of people refused to buy RTX and went with a high end 1000 series GPU, and why 1080 and 1080 Ti prices shot up. You're basically asking questions that clearly show buying an RTX was risky. This is not about the price of the GPU or whether the game was free, it's about whether going for RTX is worthwhile.
The warning for a lot of us was the video a Nvidia employee posted well before Nvidia even announced the debut of RTX or it's release date. He said RTX would take some time to be useful for players, and will be primarily a learning process for developers until it appears in enough games at good enough frame rates to be worthwhile for consumers.
Despite this Nvidia went on to embellish heavily about RTX support at their stage demo as if it would be ready at the launch of the games they mentioned supporting it, and lots of players are buying into it still, despite no real Ray Tracing support yet. You have officially bought their snake oil.