Hard to say. Way better than no helmet at all.
Top and side impact, like a Protos, is desirable.
Don't know which is better, a bike helmet for tree work, or a tree work helmet for biking. Definitely, both will help in either situation. Biking is made for ventilation through forward movement and I suspect that there are lots of openings in the top, which are undesirable with falling sticks. Ear muffs on a bike helmet are silly. A face-screen or visor is good for both, but the visor will interfere with ventilation.
Side note, Senas or similar are a big help with pull trees that require finesse, not just power. I hate working without radios.