Well it is not always what the benefits of a liner are, as sometimes in Canada you MUST have a liner by code.  And for wood burning systems that liner MUST be stainless steel  There are no options in materials.   Having said that a stainless steel chimney liner that is properly sized, for the stove, furnace, or fireplace will always maintain and often will improve the draft.  There are smooth liners, which are essentially pipes (generally 4 feet long) that are installed inside the chimney; or flexible ones which are a long continuous tube which is flexible and looks similar to a dryer vent.   The smooth wall liner will possibly be more difficult an installation, however can increase draft over a flex liner.  However, even though a great idea and a great way to reduce risk of a chimney fire in a masonry chimney, they do cost money with the liner alone costing upwards towards $1000 in many cases.    Our stainless chimney liners are generally used to upgrade and repair existing masonry chimneys. These stainless steel liner systems, when maintained are extremely safe and durable.  If your chimney is in disrepair and needs an upgrade you might want to consider a stainless steel liner as an affordable way to upgrade and get the peace of mine you deserve.

But getting back to original question, the benefits?  Over an old masonry chimney?  Safety, peace of mind, less creosote, easier cleaning, better draft, less problems with down draft (or at least easier to correct draft direction).. to name the ones that come to mind.