That is interesting. I always have heard that Rk4 is more accurate. However, that may have been a misconception because it does not allow for conservation of energy.
The question is in part "more accurate than what?" and in part "more accurate for what?"
For a linear system, explicit euler, verlet and rk4 are both perfectly accurate.
Really roughly speaking; rk4 is a fourth order method and verlet is second order. For nbody both will show a truncation error and the order essentially means that whatever the error, it will be (2^2)=4 times less for verlet if you halve the timestep while it will be (2^4)=16 times less for rk4 if you halve the timestep. Thus you can take larger steps with rk4 and get the same error (minus rounding errors) or you can take the same size steps and get less error.
So, yes, rk4 is generally more acurate... but it has a systematic error loosing energy, which verlet doesnt have, so a stable orbit will over time degrade for rk4.
At the same time, verlet can get by with one derivative evalation per step where rk4 takes 4, and that being the expensive bit, rk4 can end up losing there... depending on your requirements.
My personal favorite is PEFRL which is energy conserving (commonly termed symplectic for nbody) and also fourth order but actually simpler to implement than rk4.
All that said, we also support both fixed stepping where a frame is always a fixed step length and only one step and a globally adaptive mode where an error tolerance is given, and the integration then takes steps which are juuust small enough to respect that tolerance. That is the default mode.
Here you will not see one integrator as being more accurate than another. Instead you will see one as being faster, because it can keep the error below the tolerance with longer (fewer) steps. This can be seen in the physics step rate.
you might be interested in this video
https://www.youtube.com/watch?v=IJ2MhXUDZ6o