NOTE: This discusses autonomous car sensors but the same physics will apply to any longwave vs. shortwave sensor comparison (cost being the wildcard)
An interesting parallel is Tesla Inc.'s decision to use radar as the active component for their autonomous driving system rather than (much more common) LIDAR. My recollection of the costs/benefits of radar over LIDAR given by Tesla Inc. CEO Elon Musk in several interviews/speeches are
cost, LIDAR systems can cost 10 - 100+ times more than radar systems
penetration of certain materials, radar can better "see" through rain, dust, clouds. Or as Mr. Musk puts it
Photons of [radar's] wavelength travel easily through fog, dust, rain and snow, but anything metallic looks like a mirror.
range, following #2, radar (radio waves) travel a much further distance in an atmosphere without absorption
power consumption, each radar signal requires less power to send due to its lower frequency (a photon with a wavelength in the visible spectrum has about a million times more energy (~1eV) than one with a wavelength in the radio spectrum (~10E-6 eV). This energy had to be expended by the instrument to create each photon)
- increased resolution, LIDAR can map objects much more accurately than radar due to the difference in wavelength. Mr. Musk describes this problem with radar
A discarded soda can on the road, with its concave bottom facing towards you can appear to be a large and dangerous obstacle
As for spacecraft landing systems, they may be operating in varying environments and need the system that suits their specific situation.
Is high spacial resolution required to avoid rocks or slopes? Pick LIDAR
Is there a power or cost constraint? Pick radar
Is there dust or liquids in the atmosphere that must be penetrated? Pick radar
Does the system need to operate at a high altitude in an atmosphere? Pick radar
I would imagine an ideal system would use radar for the high altitude portions of a descent and LIDAR for final landing maneuvers.
The quotes from Mr. Musk were taken from his blog post at https://www.tesla.com/blog/upgrading-autopilot-seeing-world-radar
Below are two articles discussing the described differences in further:
Especially interesting is the following picture from article 2 showing the difference in resolution between LIDAR (whose frequency is near the visible spectrum) and radar.