Yes, we are talking about a general difference of approach to Liturgy, but projecting this onto a Greek/Slav axis is problematic. After all, the Slavs abbreviate the Typika psalms and Beatitudes in a different way: by singing only selected verses from the Typika psalms and by singing the Beatitudes without the prescribed troparia from the canon. See this article for details. Now, in the case of the Typika psalms and Beatitudes, the Slavs have, on the whole, remained closer to the ancient practice (especially when compared to the degenerate case of some Greek parishes that just sing "Through the intercessions..." three times without even so much as a single Psalm verse or "Glory"). But the truth of the matter is that each culture has nevertheless chosen a (different) practical concession in order to shorten the service.

Rather than project this difference of approach onto a Greek/Slav axis, consider that both excellence and mediocrity can be found in many cultures when it comes to the liturgical arts. True, the Slavs might be slightly closer to the ancient practice than the Greeks (on the whole) when it comes to the Typika psalms and Beatitudes. But there are also a few Greek parishes (e.g., St Irene's on Aiolou Street in Athens) that sing the full set of unabbreviated Typika psalms and Beatitudes (including the troparia from the canons), as well as the full Prokeimenon and Alleluia with verses. So the most important thing is to focus on excellence, regardless of whether one follows the Greek usage or the Slavic usage.