The biggest advantage of haylage over hay is that it is generally considered "dust free", compared to most hay products which are not.
All spores present in haylage are expanded by the presence of moisture and are bound to the grass strands this results in them being eaten rather than inhaled by the horses.
An advantage of haylage is that you don't have to soak haylage (as you would hay, particularly during the summer months when the hay is at it's dryest), which saves a lot of time, energy and water for those who previously had to soak their hay.
Haylage is even more popular with the horses due to its sweet taste, the only downside being that they tend to gobble up their night-time allowance quickly and then stand around bored - this is not good for box-walkers, weavers etc, unless you can find something else to occupy them.
Haylage nets with a tighter mesh than normal hay nets and generally have smaller capacity; this can help to slow down the greedy eaters and help deter the groom from over-feeding the horse.
Haylage is considered richer than hay, and fat ponies get fatter on haylage than they will on hay - haylage is best for working ponies only, or those with broken wind.
Its best to always buy your haylage from a reputable manufacturer and preferably somewhere or someone who has made the haylage themselves, its your horse and knowing the paper trail of how your horses feed has been produced will always give you piece of mind.
Quality is everything when it comes to haylage, so choose a company with its eye on making quality horse haylage, and ask it for an analysis of the product or even a sample (most farmers will be happy to provide this). Good companies do this as matter of course.