I've put time in on Waves API eq plug-in emulations, and also regularly use actual API hardware eqs.
I'm impressed by how well the Waves plugs do emulate the overall character and behavior of the originals, but indeed there's no comparison. The hardware considerably surpasses the software. The software does not give you the very fine distortion / harmonics of the hardware, plus, there is indeed a headroom thing going on. And in general, for whatever reason, it always seems much more difficult to dial in an eq setting with the software verses the hardware. Not sure why. It's a bit puzzling to me. But, I dread having to do critical work with plug-ins, it's always a struggle by comparison.
And regarding cheaper plug-in eqs, like the ones that come stock in assorted DAW packages... they're total garbage. I'm not going to single out any products specifically, but on several big name DAWs I've used, the stock plug-ins that you get for free with the DAW, I cannot and will not use them at all. If you think you can do good work with them, try strapping in some good hardware eqs instead, it'll blow your mind... you'll never go back.
In sum, if you can get your hands on some real hardware API eqs, do so... you won't regret it. Well worth it for sure.
Side note... while I feel the Waves API software emulates the hardware fairly well, I noted that the the 550A emulation was perhaps the least accurate. I'm used to my handwired 550As (same as the Saul Walker versions and vintage versions), these have a serious color... the software doesn't come close to emulating this... it's like maybe halfway there at best, and very watered down, not nearly as thick and creamy sounding. But the 550B emulation is more accurate. 2500 emulation not too bad either, but again, somehow I can dial up a kick ass sound way easier and faster with the hardware 2500 than I can with the software... it's weird. They're definitely not the same for sure.
I don't think digital emulations will EVER truly clone the sound and performance of hardware. I don't think it's possible. As technology improves, they'll get closer and closer, but it will never be the same. And the hardware will always have a thing about it that highly critical and scrutinous engineers will need to have. I don't think hardware will ever go away. It's worth it even just for the direct, tactile, authentic interface if anything.