Here are a few off the top of my head of wire rope vs. synthetic rope. Keep in mind this is generally speaking, as not all synthetic ropes are created equal...
Wire Rope
Pros
Durable
Can Drag On Rocks
UV Stable
Abrasion resistant
Cheap
Uses either fairlead style
Cons
Weight
Stores Energy, which is dangerous if it breaks
Doesn't float
Not flexible
Steel splinters
Difficult to fix a break in the field
Synthetic Rope
Pros
Lightweight
Doesn't store energy
Floats in water/mud
Thinner diameter means more length on drum
Stronger
Can be spliced in field if it breaks
Flexible
Easier to handle long lengths off the drum
Cons
Not UV stable, requires extra UV protection (sleeve, coating, etc.)
Can melt if exposed to heat (such as brake drum)
Subject to internal fraying by dirt and sand
No abrasion resistance, needs to be protected by sleeve
Hard to visually detect weakened/damaged rope
--Sean
Wire Rope
Pros
Durable
Can Drag On Rocks
UV Stable
Abrasion resistant
Cheap
Uses either fairlead style
Cons
Weight
Stores Energy, which is dangerous if it breaks
Doesn't float
Not flexible
Steel splinters
Difficult to fix a break in the field
Synthetic Rope
Pros
Lightweight
Doesn't store energy
Floats in water/mud
Thinner diameter means more length on drum
Stronger
Can be spliced in field if it breaks
Flexible
Easier to handle long lengths off the drum
Cons
Not UV stable, requires extra UV protection (sleeve, coating, etc.)
Can melt if exposed to heat (such as brake drum)
Subject to internal fraying by dirt and sand
No abrasion resistance, needs to be protected by sleeve
Hard to visually detect weakened/damaged rope
--Sean