I think they just want to give him a bit of a mental break for a day, as well as keep both players fresh at the other position. I don't think there's much to read into this.
I think Lawrie has better range and slightly better reaction time. Arm strength is probably about equal, with Machado a little more accurate. Machado is way WAY smoother.
None of the Jays home runs have been cheap ones off Price either. The Rays wanted to see how Price looked now against good hitters in Bautista and EE. I'd say they got their answer.