I am torn on this one. I think that a case for "sleep" can indeed be made. However, a case can also be made that we enter a conscious state immediately after death. I lean slightly to the "sleep" position and think that "today you will be with me in Paradise" does not necessarily connote a conscious state. And "to be absent from the body and present with the Lord" works with the "sleep" position when seen phenomenologically. To make a comparison: "To put my head on the pillow at midnight in a tired state is to be present with the chirping birds and sunlight streaming through the window at 8 AM.
There are too many texts which refer to the dead as "sleeping" for people to discard the "sleep" position too readily. And the distinguishing feature of sleep is unconciousness.
Besides, even if heaven is a conscious state entered immediately after death, the scriptures do not, I think, treat this as our final destination. Our final destination is in a distinctly embodied state on a renewed and transformed earth.