In general, the odometer of a vehicle will never give the same reading as the GPS. This is also true between two vehicles, or two calibrated measurement instruments.

The reality
It should be noted that car odometers are not a very precise measuring instruments, and that they have no official calibration from factory. On average, the best precision is located between -2.5% and +2.5% (possible variation of 5%).

External factors

Not only can the instrument have a reading variation, but external, mechanical and physics factors can vary the speed reading and therefore the mileage.

Among the most common factors, aside from the car’s instrument (odometer), are the tire type, size, wear, tire pressure the environment ( season) .

Some technical background
Car Speed sensors are directly connected to the transmission. Since tires can be of different dimension than the original ones from the manufacturer (EOM), tire diameter will definitely create variations.

Environmentally speaking , tire pressure will change with outside temperature, this has an effect on the final dimension.
As a matter a fact, most new cars don't use pressure sensors anymore. New car computers, along with ABS sensors are now able to detect slight rotation difference to figure out a tire is low.

Winter driving also involves slight differences in distances due to slip of tires, that will add up over time.

What you don't know about your tires

The table below provides a better understanding of why there are variations.

In this example, two models of 16-inch tires are represented
Although they are the same diameter, the are not the same same.

Compare total diameter
Tire #1 has an outside diameter 1.854m and will do 539 rotation per kilometer
Tire #2 has an outside diameter 1.885m and will do 531 rotation per kilometer

Same distance but different on odometer

The odometer is basically recording the numbers of rotation to show total distance and speed.
Logically, the more rotations, for a given distance, a tire will do, the greater the distance will be registered on the odometer.

A car equipped with tire model 1 will register more mileage than a car equipped with Model #2 tire

Tire #1 need to make 8 more rotation every kilometer
This is also reflected in the speed reading. In not 3 of the table, a speed of 110 km/h will be displayed as 111.3 km/h, a variation of 1.2%. This will also be the variation in distance.

So what does it prove ?

Under normal usage, people don't really care this much about distances . We all agree the measurement is sufficiently accurate for we we use it for , and the % is not significant enough to create any problems.  Police radars are accurate and calibrated instrument, and this is the reason the police will consider a small % gap between the radar and what the driver would read in is car.

So who is right ?
Since 2000 the US army had removed the purposeful degradation of the GPS signal , giving the public a more precise system, that in many cases are down to a meter precision.

GPS calculates distance and speed based on coordinates sample taken at a constant time.

Compare the 2 coordinates between cities

Montreal  45.5017° N, 73.5673° W

Laval        45.8782° N, 73.2849° W

total distance in a straight line  = 47.28 kilometers NW

If you take thousands of small samples along the way, you can calculate small distances and add them up in the end.
This will get a  precises final distance of a trip ( because trips are never in a perfect line )

Keep in mind there is also a small margin of error while calculating distance

The human factor

The user is mostly responsible for the GPS variation

For example,
What is the GPS is not always in use
What if the GPS is not ready when he starts to drive ? There is always a few yards that could be lost here and there ...
What if it was disconnected at some point and the user was driving the vehicle without the GPS.

It is nearly impossible to fully be certain both instrument are perfectly synchronised

Conclusion
From the previous explanation about tire size and total distance and how the GPS reads distance , we can agree that you will never be able to fully match both the odometer and GPS.

You can be confident the GPS is doing as good of a job as the odometer, even if they don't seem to match.

GPS are recognised as precise measurement instrument with limited external factors that can influence them.

We seldom refer to the TL1000 as an "instrument" as opposed to a "device" or "logger" because it is a precise measurement instrument.

What you must know
In general, when there is a difference, the odometer VS GPS accuracy is seldom in favor of the GPS.
There is no evidence that the odometer of one particular vehicle is more or less accurate than another, unless a precision calibration would be performed on both vehicles.

TripLogik, uses the largest antenna available on the market for its size, allowing the instrument to receive the maximum signal and be as accurate as possible with current technology.  Of course, the latter must be positioned as recommended in the installation manual and the accuracy may vary depending on the conditions.

Some articles make by different new media about this subject,