I would not say the OT isn't used by the byzantine practice. Just the opposite, the OT is the basis for the services. There is a book that I havn't seen in some time now called the bible and the litrugy. It is a look at every single line of the Liturgy of St. John Crystosom and the how it relates to the bible.
Something else to keep in mind is that the bible is broken into more parts then just 2 (old and new). In the NT you have the Gospels, the Epistles, and Revelations. The epistles readings are regulated to just the Liturgy while the Gospel readings are found in the Liturgy and Orthros and in Compline during the first week of Lent and at the Agape Vespers. Revelations is never used as a reading during the services but elements from that book can be found embedded into the text of several of the services and prayers.
The OT is the most used in regards to using it for the text of the service. The Psalms are incorporated into every service. Then eintire is Psalter is actually said each and every week (twice during lent) during the complete cycle of services. The books of prophecy are used at at any feast of Saint where the polyeleos is prescribed, which is around 80 days of the years doing a quick count of the typikon. When these are read at Vespers there are usually at least 3 readings. During Vepsers of lent there is a reading from Genensis and a reading from Proverbs.
This is part of the reason the services outside of Liturgy are so important in the Orthodox Church.
Hope this helps.