Which type of games is more suited for users on mobile platforms (phones, tablets) considering their thumbs movement?
LEFT TO RIGHT like in R-Type?
or BOTTOM TO TOP like in Xenon?
I'd go for bottom-top, because that would avoid right-/left-handedness issues. (Also personally, I find sideways movement of the thumb easier than up-down, but clearly that's only anecdotal evidence.)
Could It could work in both orientations?
If you had to limit it to one. Fix the orientation and work in whichever is the "longest" Example:
If its mobile portrait (go up and down) If its mobile landscape (go left to right)
I think the limited space is the main factor that would effect playability. You need to take advantage of the orientation that allows the most room between one end of the screen and the other.
With regards which is best, I'm not sure. Some users seem to have preference for vertical shooters while others prefer horizontal. Personally I feel that vertical shooters work better when you are dealing with quick reactions and can take multiple hits. Where as horizontal works better for me with precise movements.
Also need to take into consideration whether the game needs any UI controls (on screen joypad) or is based on swiping movements.
I think most users expect to be able to choose between touch and accelerometer, and it may be easier for users to manipulate the device when it is held in landscape view with two hands if used with accelerometer.
Subjective, but I would go landscape with bottom to top scrolling.