Large textures or small textures? What brings the best performance?

Is it better to use many small textures for the background of a 2D side scrolling game instead of one large texture?
My large texture measures 1500x1500 pixels. Is it better to split it in 25 small textures(each texture 300x300 pixels) for a better performance on Windows Phone/iOS?
How can I measure the frame rate of my game?

The best solution is to minimise the number of textures and the number of meshes. In some commercial titles, they do a post processing on their game data to combine meshes and textures in the same scene. This might not be feasible for a smaller developer, so you could chose a middle ground that has several texture atlases that still allows you to make changes where needed while developing the game.

I have no 3D models, just many Sprites(Texture2D). Is it possible to see how much memory is used by the game? Because sometimes when loading the sprites I get an error message that says that my device is out of memory. I have a Nokia Lumia 920.