Help with drainage area between new patio slab and driveway.

Need some professional advice.
We just had a new stamped concrete patio poured. The raised part had already been there & the slab was replaced, but the lower part is new (SEE PHOTO). After discussing water drainage concerns with contractor about having that much concrete near the foundation of home with basement, we decided to leave an area between the driveway and the new part of the patio that is on grade for the water to go as it runs off of the driveway...(the patios slope heads off the front of it).
We are trying to decide whether it is best to just plant grass in that area, or add a piece of edging parallell to it and create about a 2 foot planting area filled with decorative stone along it.
I am wondering which would be best considering that during heavy rains that area will get a lot of run off and we are in Michigan so have freeze thaw considerations. I am thinking that by leaving dirt/grass against it, the freeze may keep pushing against it and may create heave eventually whereas gravel against it may have a little more give.
Professional Opinions? (ps.don't mind ugly cinderblock, its a work in progress - any suggestions for that? trying to figure out products to use to match that to the color of the rest of it)
Thanks in advance!

Thanks for the advice. Grass it is then.
I realize that it will move no matter what, but just thought that if we maybe had gravel next to it vs. compacted dirt w/grass that maybe when its frozen in the winter, the gravel might allow for a little more movement than compacted frozen dirt up against it.
There is a relief cut by the way.
Thanks again for your help!

Debbie, I would plant some Pampas grass or some kind of ornamental grass to add some interest.