A recent literature review in Clinical and Experimental Optometry called “Ocular and visual discomfort associated with smartphones, tablets and computers: what we do and do not know” (Jaiswal et al, Jan 2019) compares what has been scientifically established to date about the connection between dry eye and computers versus dry eye and smartphones & tablets:

Tear volume: Computers decrease it; not enough evidence yet about whether handhelds do.
Blink rate and amplitude: Consistently reduced with computer use. but data are contradictory for smartphones and tablets.
Tear stability: “May” be adversely impacted by computers and handhelds.

Surprisingly:

The available literature does not conclusively link eye and visual discomfort symptoms reported with handheld digital devices, with changes in binocular vision, blinking or ocular surface

And, uh, yes I daresay:

studies are required in high users such as teenagers, and in patients with dry eye

They mentioned several factors that may explain differences in how computers affect us versus handhelds, including:

Position
Distance
Screen size
Luminance
Patterns of use