The autopilot for me was not doing a good capture on either Localizer or regular VOR.  It would tend to overshoot the centerline and come back on course.  This wa a known "feature" for several FS versions.  I had some mods that I tried and now it works perfect for me.  

Here's the AUTPILOT section of the aircraft.cfg file.  Each line that is modified below has the old value indicated.  Try this if you like but make sure to back up the original first.

Also note that the max bank angle was 30,25,20,15,10 but that was only useful for the default 737-800 which has a switch to select the max bank angle.  I chose 25 and it seems to be perfect. The changes should be noted in RED.

autopilot_available=1
flight_director_available=1
default_vertical_speed=1800
autothrottle_available=1
autothrottle_arming_required=1
autothrottle_max_rpm = 90
autothrottle_takeoff_ga=1
pitch_takeoff_ga = 8
max_pitch=10.0
max_pitch_acceleration=1.0
max_pitch_velocity_lo_alt=2.0
max_pitch_velocity_hi_alt=1.5
max_pitch_velocity_lo_alt_breakpoint=20000.0
max_pitch_velocity_hi_alt_breakpoint=28000.0
max_bank=25                  //was 30,25,20,15,10
max_bank_acceleration=1.8
max_bank_velocity=3.00
max_throttle_rate=0.10
nav_proportional_control=17.00   //was 12.00
nav_integrator_control=0.01      //was 0.25
nav_derivative_control=0.00
nav_integrator_boundary=2.50
nav_derivative_boundary=0.35     //was 0.00
gs_proportional_control=25.0
gs_integrator_control=0.53
gs_derivative_control=0.00
gs_integrator_boundary=0.70
gs_derivative_boundary=0.00
yaw_damper_gain=1.0

As in all updates/tweaks, YMMV.  ;D

Phill