We estimate position of robot in localization and SLAM. My intuition says we get better position estimation in localisation than in SLAM because we have better sensor model likelihoods in localization because of given complete environment than in SLAM.
I would like to know the difference in accuracy of estimated position in localization and SLAM.
Localization has the goal of identifying where a robot is within an environment. Whether you have an accurate representation of the environment already or not is the distinction you are trying to compare.
It seems the accuracy of your position would be contingent on the accuracy of the mapping you can build. In a fixed indoor environment with few obstacles and high definition sensors like LIDAR it would seem you could create a very accurate map and the difference in accuracy between the approaches would be null since both maps would be the same. The complexity of the operations to get there is different, but the accuracy seems like it would be the same.
If you are in a complex and changing environment it would be a different story. The map you had cached using localization alone may no longer be accurate for path planning or navigation you would get from a SLAM approach.
If you trust your map and you trust your sensors (dead reckoning, odometry, gps) as to where the robot is in the environment than I suppose it follows SLAM would not yield any additional accuracy.
Your intuition is good. SLAM and a-priori map localization both use (roughly) the same technique for localization, but your SLAM position is only as good as the confidence you have in your map.
With an a-priori map, the confidence in the map is 100%.
There is no meaning of this kind of comparison. It is evident that the localization will be more accurate than SLAM. Let's see why. SLAM is usually constructed by using probabilistic methods as follows $$ p( x_{t}, m | z,u) $$
One seeks to solve the aforementioned conditional probability where $x$ is the state vector, $m$ is the map, $z$ is the observations and $u$ is the control input. For localization, also by using probabilistic methods is as follows
$$ p( x_{t} | z,u, m) $$ You will notice the $m$ in localization is provided which means the true location of the map is known with absolute certainty. This is not the case in SLAM in which we need to estimate the map $m$ which means the absolute certainty is not provided (i.e. impossible to access to the true location of the map). In SLAM, more work need to be done to filter this noise. As you can see, loosely speaking, localization is a simplified version of the SLAM where we assume the map is given. This is why the authors of "Probabilistic Robotics" started the discussion with localization before SLAM. That being said, SLAM is more realistic than localization.
