The main reason for the two types is historical, supporting the existing phone base in different IP Office markets.
The IP Office suite is a development of an non-Avaya predecessor called Network Alchemy.
Network Alchemy was taken over by a UK company called SDX, whose phone systems used DT phones. Thus support for DT phones was added.
SDX then became part of Lucent/Avaya and support for DS phones was added.
As for which is better - hard to say, they all have their strength and weaknesses. The range of phones useable with a DS port is a lot broader and will probably keep growing would be my thought with DT becoming more of a legacy feature.