One problem with measuring RF power in an antenna system is that there are a number factors which can cause erroneous readings, these being distinct and separate from the basic accuracy of the meter.
Factors which can mess up a watt meter reading are SWR, impedance mismatches, and unwanted single ended currents caused by an unbalanced system.
There are different types of watt meters available which use different types of internal circuits to provide a measurement. Each type has it's own level of inherent protection against system problems.
Watt meter types include those that use a diode detector, a bridge circuit, directional coupler, thermocouples, and others.
For a perfectly matched antenna system most watt meters will give a reasonably accurate reading. Where an antenna system has an impedance mis-match is when lower quality meters will give a more inaccurate reading.
As an example, for an antenna with a bad SWR fed with coax, the reading shown on a cheap watt meter will change depending on where along the line the meter is fitted. This is because the meter power reading is affected by the line impedance, which changes along the length of the line for a system which isn't perfectly matched. A better quality meter will be less affected by line impedance.
Generally speaking, the more expensive a meter is, the less the reading will be affected by system problems such as impedance mismatch.
Then in addition, there is the basic accuracy of the meter which can be considered, which depends largely on the value tolerance and temperature coefficeint of the internal components.
If you just want a general relative reading that is say plus and minus 10 %, the internal meter in your radio is probably good enough, or you can get away with a cheap external watt meter.
More expensive meters will probably be less affected by impdance mismatches.
If you need to get readings which are absolute in accuracy, then more expensive lab instruments would be better.
In general it seems that older style ham radio watt meters from 1950 - 1970 are better than newer models.
Hope that helps !