A recent article appearing in Sciencing.com by Philip J. Carlson; Updated April 24, 2017, entitled "PH Meter Versus PH Paper," addresses the question posed directly: "Measuring the pH of a substance can be accomplished in a number of ways. A pH meter is one of the most common methods, and pH paper (also known as litmus paper or pH strips) is also a quick way of finding the pH of a substance. There are a few other ways that are commonly used, including titration, but most are tedious and require detailed hands-on work.
THE PH METER
The first glass pH electrode was constructed in 1908 by Fritz Haber and Zygmunt Klemensiewicz. As the paper describing the electrode was published a year later, it is usually assumed that the electrode was created in 1909. A pH meter has a membrane that allows acidic ions (H+) to pass through it creating a voltage. The meter associates each voltage with a particular pH value. The higher the concentration of acid, the more ions that will pass through the membrane thereby changing the voltage that is created. This voltage change will be interpreted as a higher pH value.
"It doesn't pass the litmus test" is a common phrase that has its origin in the use of litmus paper for pH detection. These strips of paper are impregnated with pH indicator molecules that change color upon contact with solution of a particular pH. Each color is indicative of a particular pH value. The paper is compared to a standard chart where the colors are compared and then associated with a pH value.
ACCURACY OF THE PH METER
A pH meter is normally assisted by the use of a computer or a digital user interface. They are calibrated by the use of standardized buffers which allow the meter to associate a particular voltage with a pH value. There are subtle differences between pH meters, but they are generally accurate at least to the hundredths place. These meters can be sensitive to ion interference, from various ions in the solution you are testing, and are known to drift from their calibrated position after some time. As long as they are treated with care, calibrated regularly, maintained according to the manufacturers recommendation, and stored correctly you can expect a pH meter to be accurate and durable.
ACCURACY OF PH PAPER
The use of pH paper can be likened to the use of a Galileo thermometer. Particular colors indicate certain values and each measurement is only accurate within a unit or two. While pH paper is great for quick qualitative work it fails at highly accurate quantitative work. If the accuracy you desire is within one pH value or two, paper is the way to go. Litmus paper can give you a quick check to see if your solution is acidic, neutral or basic. That is one place pH paper shines. On a side note, pH paper will be difficult to work with accurately if you are color blind.
If size and bench space is a concern, pH papers come in a small canister which is no bigger than a bottle of prescription pills. Meters on the other hand can take up space about the size of a laptop computer, and some can reach into the air about a foot and a half. Cost is always an issue to consider. Litmus paper will cost you about $10 while an electronic pH meter can be anywhere between $50 and $800."