as above theyre cheaper, lighter, and easier to install for the tradesman (likely why it was suggested). That being said, the cost of works is:
cost of door
cost of hanging door
cost of painting door
one way or the other, youll pay the same price to hang the door regardless of it being solid or honeycomb. assuming that you dont use a prepainted/prefinished ornamental door, the cost of painting will also be the same for each.
so for arguments sake, lets say that your costs are:
honeycomb door: $70
solid core door: $200
hanging door: $80
cost of painting door: $80
then your two scenarios are:
honeycomb: 70 + 80 + 80 = 230
solid core: 200 + 80 + 80 = 360
difference: 360 - 230 = 130.
So the question you need to ask yourself is whether or not the extra $130 is worth having a solid core door that will certainly last a lot longer, certainly be easier to work with long term (you can add deadlocks, latches, peepholes, whatever at leisure), and provide better protection for your tenant/yourself. (I can personally put my foot through a honeycomb door and break into a place in all of 15 seconds if i felt like it)
just so you know, Im in Darwin, my prices are different to yours so add in your own numbers. I just wanted to share how I think about such things