I recommend the Armytek Wizard Magnet USB with XP-L LED (NOT the more expensive XHP50 version, it’s too floody). It has an almost perfect beam for running and has all the features and comfort you could ever ask for. If you search around for a good deal you should be able to get it for a fair price ( ~60$ is good).
The beam is so good because of the TIR lens with built-in hexagonal diffusor. In combination with the correctly sized LED it produces a very good beam for running. There is no real hotspot. It’s just brighter in the center. Ther is no “bouncing spot effect”, no tunnel vision. The spill does not have a hard outer edge like some reflector lights have. This also reduces the tunnel vision effect.
It produces 390 lumens for 3.8h on one 18650 (second highest mode). I consider this mode the best one for running. It’s bright enough. There is also a warm-neutral white version which is slightly less bright.
Because of the Buck-Boost-driver it also works better in winter when it is cold compared to other headlamps. It will keep the brightness constant even when the battery has a reduced voltage because of the cold. The integrated over discharge protection also allows you to use unprotected high-drain cells like the Samsung 30Q. These offer much better performance in cold temperatures compared to standard high-capacity cells.
The current Amrytek headlamps have a new plastic holder which is much better compared to the older style silicone holders. They are very comfortable (ergonomic shape) and the light doesn’t wobble at all when running. It also allows you to instantly remove the light for hanging the headband out to dry or when you want to use the light handheld (it’s also a very practical edc flashlight). You can also easily adjust the angle of the light in the holder with one hand.
The included magnet USB charger allows you to charge it on the go with any usb charger you have on hand (it’s pretty slow though).
I know only one headlamp with an even better beam for running: the Olight HS2. At the same ~400 lumens it has an even wider spill and also more throw. But there are lots of tradeoffs. It has less modes, the driver buzzes next to your ear, it doesn’t use 18650s, no 1000 Lumen turbo mode, wobbles a little bit, a bit more expensive, cannot be used as a flashlight etc.