… met Aarti Khale ji at Rani Baug on 9 FEB 11: …………………………..

– Based on molecular analysis as well as morphological differences, by the top experts of the world, the order LILIALES was broken down into three
Asparagales included many of the families, like Orchidaceae, Boryaceae, Blandfordiaceae, Lanariaceae, Asteliaceae, Hypoxidaceae, Ixioliriaceae, Tecophilaeaceae, Doryanthaceae, Iridaceae, Xeronemataceae, Xanthorrhoeaceae sensu lato, Hemerocallidoideae, Xanthorrhoeoideae, Asphodeloideae, Amaryllidaceae sensu lato, Agapanthoideae, Allioideae, Amaryllidoideae and Asparagaceae sensu lato.
Asparagaceae inturn was divided into sub families which included many of the earlier families such as
subfamily Agavoideae = family Agavaceae and family Hesperocallidaceae
subfamily Aphyllanthoideae = family Aphyllanthaceae
subfamily Asparagoideae = family Asparagaceae sensu stricto
subfamily Brodiaeoideae = family Themidaceae
subfamily Lomandroideae = family Laxmanniaceae
subfamily Nolinoideae = family Ruscaceae
subfamily Scilloideae = family Hyacinthaceae
Cordyline belonged Laxmanniaceae which is not under Asparagaceae where as Dracaena belonged to Ruscaceae and earlier Ruscaceae did belong to Liliaceae but that was loooooong time back and not any more.
Some of the basis differences are provided in Wikipedia which are given below.
The order is clearly circumscribed on the basis of DNA sequence analysis, but is difficult to define orphologically, since its members are structurally diverse. Thus although most species in the order are herbaceous, some no more than 15 cm high, there are a number of climbers (e.g. some species of Asparagus), as well as several
genera forming trees (e.g. Agave, Cordyline, Yucca, Dracaena), some of which can exceed 10 m in height. Succulent genera occur in several families (e.g. Aloe).
One of the defining characteristics of the order is the presence of phytomelan, a black pigment present in the seed coat, creating a dark crust. Phytomelan is found in most families of the Asparagales (although not in Orchidaceae, thought to be a sister to the rest of the group).
Almost all species have a tight cluster of leaves (a rosette), either at the base of the plant or at the end of a more-or-less woody stem; the leaves are less often produced along the stem. The flowers are in the main not particularly distinctive, being of a general ‘lily type’, with six tepals, either free or fused from the base.
The order is thought to have first diverged from other related monocots some 120-130 million years ago (early in the Cretaceous period), although given the difficulty in classifying the families involved, estimates are likely to be uncertain.
This order consists mostly of herbaceous plants, but lianas and shrubs occur. They are mostly perennial plants, with food storage organs such as corms or rhizomes. The family Corsiaceae is notable for being heterotrophs.
The order has worldwide distribution. The larger families (with more than 100 species) are roughly confined to the Northern Hemisphere, or are distributed worldwide, centering on the north. On the other hand, the smaller families (with up to 10 species) are confined to the Southern Hemisphere, or sometimes just to Australia or South America. The total number of species in the order is now about 1300.
One big question raised by someone was, why Dracaena or Cordyline is in Asparagaceae and not Liliaceae.
Classifications change from time to time. When Linne wrote Species Plantarum, he had his limitations in escribing a taxa, he didnt have much facility and hence if you see his descriptions, trust me, half of the plant a common man wont be able to identify. For example, he described two taxa as
Dioscorea alata: follis cordatis, caule alato bulifero
Dioscorea bulbifera: follis cordatis, caule laevi bulbifero
Linne didnt have a proper microscope. But then things improvised and more and more technology got involved and people started describing species in more details and then finally is the age of DNA which some Indians have just started using. Though world has reached PROTEONOMICS which India is still unaware of.

– I got this reply from …, still waiting for reply from Vienna.

Most Asparagales have phytomelan in their seed coats, except for orchids (microseeds with thin seed coats, so no room for phytomelan) and some Asparagaceae (such as Convallaria with a berry, but Asparagus itself does have phytomelan even though it has a berry). No Liliales have this. Liliales has nectaries no located in the septae of the ovary, whereas this is common in Asparagales. There are differences as well in pollen and ovule development , but these are technical. Spotted tepals are frequent in Liliales (as in Alstroemeria and Tricyrtis), but this does not occur in Asparagales, and in the latter blue flowers are common, whereas in Liliales they are rare.”

Its really good to get enlightened by subject authorities.