Which is more visible....Strobes or Steady Incandescent lights?
There are numerous variables. Omnidirectional strobes (normally xenon filament) are generally brighter than omnidirectional incandescent lights (usually halogen) but this depends on the strobe capacitor and amperage. Omnidirectional lights are typically used at the summit of an obstruction.
Unidirectional lighting (brighter through the use of focussed beam shaft and base reflectors) again tend to be brighter in daylight with the use of high amperage strobes although similar lighting intensity can be achieved with halogen lamps but they are generally not used at the brightest power levels as they burn out too quickly.
Strobes therefore are generally better for both omni and unidirectional lighting (during daylight hours) but incandescent lighting is better at night in both roles because it is less distracting. High amperage strobes at night are a distraction and those which are used for this purpose are generally lower power or possess a photoelectric cell which switches the power source through a different (lower amperage) capacitor.
On a day with decent vis...but some Haze....Strobes can be seen a fair ways off....so long as there is not a brighter or more conspicuous light behind them when viewed from the Aircraft.
This again depends on the type of strobe used (Crystal Palace has the high intensity [high amperage] type) but, far more importantly on the fog/cloud density. If there is partial fog yes, they can penetrate over some considerable distance as with low density cloud/fog. If the fog is dense then you will get the luminescent cloud I mentioned and which dissipates within a few metres.