I was thinking of the advantages of both calendar systems. I can come up with tons of advantages of solar calendar - biggest of them would be to mark the start and end of seasons, which governs/controls agriculture, farming, mating and breeding cycles of animals and what not. Basically the foundation of global economy depends on the factors that can easily be tracked through solar calendar.
Not only that, solar cycle is more predictable and needs one adjustment every four years, as compare to the lunar cycle which is random (29 or 30 days) on monthly basis.
Only advantage of lunar calendar that I could think of, would be to know the full moons nights that could be useful for the small marine and fishing industry (to avoid high tides), for old days travelers (to take advantage of the light during night and continue traveling) and sane people to avoid lunatics men and h/w (hormonal wives and/or howling wolves).- who go crazier during full moon nights.
Not only that, solar cycle is more predictable and needs one adjustment every four years, as compare to the lunar cycle which is random (29 or 30 days) on monthly basis.
Solar calendar became predictable (accurate) only when scientific knowledge was used to make calculations. Otherwise there were huge discrepancies happening every few hundred years. Think about addition of the months of July and August (Julian calendar), and then another significant adjustment about 500 years ago by that priest (Gregorian calendar).
Lunar calendar also needs scientific knowledge to make it accurate and predictable. Problem is our mullahs who have no problem counting seconds as predicted by scientific calculations during roza, but would follow one single hadith very literally to actually "look" for moon to announce the next month. This is what makes lunar Islamic calendar almost useless except for its use in religious ceremonies.
With proper calculations, lunar calendar could be very accurately predicted for the next year ... and then people can use this calendar to set dates for their meetings.
lunar calendar is easier if you are a nomadic or hunter-gatherer society, it is the simplest way to keep track of periods of time. but once you discover agriculture, and periodicity of cultivation seasons upon which your entire civilization is built, the solar calendar takes over.
I think that Lunar way is easier to keep track of the day of the month because you just need to look at the moon (size and presence) to figure out which day of the (lunar) month it is.