When efficiency of solar cells or solar panels are talked about, always keep in mind that this has something to do with size. The majority of all solar cells come with an efficiency rating. To understand this right away, just compare a 200Wp high efficiency vs 200Wp low efficiency solar panel. They both produce the same potential amount of electricity which is 200Wp. The only difference is that the high efficiency panel is smaller in size than the low efficiency panel. If you have enough roof space or ground, it does not matter whether you use high or low efficiency panels as long as you reach your required output power.
Efficiency of solar panels are identified in percentage. Monocrystallines usually are rated at a range of 15 to 20+% while polycrystallines are at 13 to 16+%. Panels that are made of monocrystalline cells are almost always smaller in size when compared to a polycrystalline panel with a similar capacity in terms of Watts (Wp). And if the monocrystalline panel is of the same size as that of the polycrystalline panel, the difference would be on their output (Wp), the monocrystalline would most certainly have a higher Wp rating. A simple example in a real world situation would be a PV system that requires 3kWp of panels output and that the roof is the only choice of mounting the panels and that it can only accommodate 10 pieces of a panel with roughly the size of 1600mm x 1000mm. A polycrystalline panel of that size would be at a range of 250Wp to 265 Wp as compared to a monocrystalline panel of the same size that can reach up to 300Wp. This means that the contractor would need around 12 pieces 250Wp polycrystalline panels to meet the power requirements of the house but those 12 panels will not fit on the roof and so the best choice would be to use the monocrystalline ones which only 10 panels are needed to attain the 3kWp requirement.
The leading solar manufacturer today in terms of efficiency is Sun power. Their solar module efficiency rating is slightly above 20% and they hold the record for reaching such value. The rest of the solar panel brands out there are usually below the 20% mark.
It is good to note that there are solar cells that reached 46% efficiency but that they are solar cells in a different category, specifically concentrator triple junction, and that they are too expensive for residential and even commercial use. The leading manufacturer in this higher category is Soitec and Fraunhofer Institute and these types of cells are used in space by NASA where just a small area is very important hence the need for the most efficient solar cell.