When it comes to birth photography the equipment you choose to shoot with matters a lot. Normally I would say the camera doesn't make the photographer anymore than a fancy kitchen makes for a great chef, but with birth it's a little different. Birth sessions are unpredictable and usually occurs in small, dimly/artificially lit spaces. I need equipment that works well in challenging environments and responds without hesitation. Every piece of equipment I shoot with was chosen for it's capability to perform well in any birth environment. I shoot stills & video simultaneously to help not miss a moment, plus if one camera starts having issues (which does happen--technology can be finicky sometimes) I can easily switch and document both stills & video on one camera as a backup.
I bring TWO Nikon D800s and a point-and-shoot Nikon with me to every session. One of the reasons I chose the D800 was because it had amazing reviews for working well in low light. My favorite lenses for birth are the 35mm 1.4, 24-70mm 2.8 & 50mm 1.4. I also bring several dozen batteries, a charger in case of a marathon session, plenty of high-speed memory cards and backup high speed memory cards. I also carry a speedlight flash and a dual camera harness to help carry it all. I also have an 85mm 1.4 that I've had with me since the beginning of my photography journey over 12 years ago. I don't use the 85mm very much unless I'm shooting a portrait and I've thought of selling it, but it's so sentimental. I'm not quite ready to part with it.