It depends. I have a very large room in my house that has a lot of furniture. I like having a very wide field of light in that room instead of a bright directional light. For the rest of the house I prefer more of a directional bright light.
During clearing operations I used a helmet mounted light for looking around and a issue Surefire on the rifle. The SF while heavy, threw out a huge near sun like directional beam while the head light allowed me to do a number of other things without lowering my weapon or using another hand. The arrangement worked very well and I have essentially adopted it for home use.
So for HD my suggestion would be both. A weapon mounted light with a high intensity directional beam and wider head lamp beam.
For SD I don't carry a weapon mounted flashlight, just my regular flashlight on the belt. For my plans this is adequate.
Tomorrow is the most important thing in life. Comes into us at midnight very clean. It's perfect when it arrives and it puts itself in our hands. It hopes we've learned something from yesterday.