This is a very interesting question, and really difficult to answer at the same time. I have tried to interpret the "experience of driving" from different angles. Hopefully one will apply to your use-case. I list the papers, and describe why I chose them. I could not find freely available papers in all the cases, unfortunately.
Where do drivers look while driving (and for how long) (2002) (full PDF)
As a baseline of existing human factors research concerning driver experience, I found this excellent chapter that is specifically geared towards fixation (eye-tracking). I am not an expert in the field, but I would hazard a guess that a lot of these findings would apply to both LHD and RHD scenarios. It is really interesting reading (30 pages or so). Some of the questions that they ask (and answer), include:
- Does visual demand actually relate to crashes?
- Does looking at an object guarantee that the object is noticed?
- What is typical looking behaviour?
- Where do drivers look when driving curves?
- How do traffic and other external demands affect where drivers look?
- How does glance behaviour change with driving experience?
- How long can drivers look to the vehicle interior?
Then I thought about how being right-handed, or being trained to drive on the right side of the road may affect navigation inside and outside the car (e.g. while walking). It turns out that there are a lot of right-hand/left-hand studies that ask similar questions.
Right-Handers and Americans Favor Turning to the Right (2002) (Abstract)
We tested a finding by E. S. Robinson (1933) that people have a bias
to turn right upon entering a building. We hypothesized that this bias
is attributable to learning derived from traffic rules that specify
driving on the right side of the road and that it also could be
related to handedness. We tested participants in both the United
States and England in a simple "T-maze" task in order to compare their
directional preference. Handedness was the best predictor of
participants' directional preference. However, U.S. participants also
were statistically more likely to turn right than were English
participants. The preference to turn right was not found to be
significantly related to eye dominance or reading direction of the
primary written language of the participant, although in the case of
reading direction, the sample size of right-to-left readers was too
small to be conclusive. The findings support that walking direction
preference is an additive function of both learned driving patterns
and genetic handedness. These findings have practical implications for
the design of public spaces such as schools, businesses, and urban
There are some interesting related studies on where people choose seats in movie theaters based on handedness, and also on airplanes that you could look into for a broader context.
Then I stumbled on two scenarios that could help, but are more related to safety studies. The first, considers situations where right-hand-drive vehicles are operated in left-hand-drive environments, and the impact on the driver's ability (measured through number of accidents)
The safety of vehicles imported from right-hand-drive vehicle configuration countries when operated in a left-hand-drive vehicle environment (2009) (Abstract)
The concern with these vehicles is two-fold: first, does the RHD
configuration lead to increased risk of crash involvement; and second,
are these vehicles inferior in comparison to built-for-Canada vehicles
of a similar age, with respect to occupant protection potential?
In this study three separate methodologies were utilized in
approaching these concerns: a relative crash culpability analysis
where RHD and left-hand-drive (LHD) crash rates were compared for the
same group of drivers; a survival analysis where time-to-first-crash
was compared between RHD and LHD drivers: and a multiple regression
model where RHD vehicle driver risk was compared to that of a
similarly constituted comparison group of LHD vehicle drivers.
The results of all three analyses were consistent. RHD vehicles had a
significantly greater risk of at-fault crash involvement over that of
similar LHD vehicles. However, crashes involving RHD vehicles were no
more severe than those involving LHD vehicles only.
The second scenario involved designing guidance systems for drivers who normally drive on the right side, but visit Japan (where the law requires driving on the left). Again, I find that the "switching" of sides is more interesting than picking either one side above another.
Study of in-vehicle route guidance systems for improvement of right-side drivers in the Japanese traffic system (2010)
A country can adopt one of two standards for traffic flow — cars may
travel on the left or right side of the road. When drivers who are
accustomed to driving on the right side of the road drive on the left
side, and vice versa, the mental workload is likely increased due to
the driver’s unfamiliarity with a new language, the position of the
driver’s seat, different driving directions, and other factors that
differ from those of their home country. One method of doing this is
to make sure that the in-vehicle route guidance information (RGI) is
not overly complicated — thereby assisting drivers in improving their
safety. Consequently, the aim of this study was to facilitate mobility
and improve safety for natural right-side drivers driving temporarily
in left-side traffic. In this study, driver behavior and workload —
given various types of RGI — were evaluated in a driving simulator
with a variety of prescribable test conditions. This research was
composed of two experiments. In the first, various types of in-vehicle
route guidance systems were tested and evaluated in terms of their
characteristics and associated driver behaviors (while driving). In
the second experiment, systemic factors and effectiveness were
evaluated by two combined systems, arrow and map-type information,
based on the results of the first experiment. In light of both
experiments, the various types of route guidance systems were
discussed in terms of their results. A navigation system was proposed
to alleviate some of the secondary tasks such as route selection.
There is some other really interesting research concerning navigation and route planning, and how people interpret maps and are biased in selecting routes based on their perception of north and south, but I guess that falls well outside your original question. Still, I couldn't help but wonder how it relates to our handedness and driving position in some subconscious way.