It is not the tripod. A good sturdy tripod works well for both. It's all about the head on the tripod. For binoculars most glassers prefer a good ball head. If you are using a spotter then a good fluid head would be the bettere option. Feel free to call me to discuss the options at 516-217-1000
The way the head mounts to the tripod should be the same. Different heads will come with different style of mounting plates to mount the camera or binos to the head. One thing to look for is how much weight the tripod can hold. The more weight it can hold, the more sturdy it will be. I use the same tripod for my camera and spotting scope. If I’m hunting I will use a fluid head. The rest of the time I have a gimbal head on it for my camera and I also have a second mounting plate that I can put on the spotter and use it with the gimbal. Honestly like the gimbal for my spotter better then the fluid, but it’s a little heavy. A ball head would be best for binos.