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It's faster in my scenario. YMMMV.

Not in the specific models I looked at.

I personally use a Linksys WRT3200ACM.

https://openwrt.org/toh/linksys/linksys_wrt3200acm

DD-WRT is has access to some proprietary (Broadcom?) code which enables NAT acceleration on some models which, at least in my case, greatly improved performance over OpenWRT.

Exactly. They have signed an NDA with Broadcom: https://openwrt.org/meta/infobox/broadcom_wifi

"DD-WRT has a license agreement and NDA in place with Broadcom that allow usage of better, proprietary, closed source wireless drivers (binary blobs) which they are not allowed to redistribute freely."