The speed of a procedural shader is dependent on the algorithm used (ie: what does the shader do).
If it's a simple gradient, then the procedural will be quicker as it's faster to do a multiplication between two cached colors than to look them up in another source and pull the data across the bus. When you use bitmaps or other cached data, mental ray has to allocate memory to hold the data and that can be a slow process. As storage requirements increase, efficiency decreases. Allocating 1000 bytes of memory will not be 10x slower than allocating 100 bytes of memory, if anything it'll be around 12x or more (exaggerated example) because mental ray has to search more of the RAM/harddrive for available space. Since memory isn't used linearly, mental ray will have to size up each free chunk it finds before it decides whether it's usuable or not - that takes a lot of time, especially if your memory/harddrive is fragmented or near capacity. mental ray (or any software for that matter) also has to free the memory when everything is done - another big hit, but not as big as allocating and initializing.
If the effect being computed is fairly complex involving many recursive computations such as fractals, reflections, refractions, anti-aliasing, or situations where intermediate data needs to be generated before final results can be computed, then the bitmap approach can be faster as bitmaps usually are used for providing pre-computed data (assuming the bitmap doesn't overly consume memory).
To summarize: The answer is very arbitrary and varies from case to case. Just because a bitmap shader runs fast in a simple scene doesn't mean it will run fast in a complex scene (same for procedurals). When you find something that works to your liking, besides saving presets, make sure you take notes as to the conditions in which the shader is run (eg: big scene vs. small scene, available memory, scene contents - lots of models, how much animation data, etc...). Over time, if your disciplined, you'll have a nice log of data to cross reference for when you start moving into unfamiliar territory in future projects.
If you want the nitty-gritty as to which is faster and why - then start reading the mental ray manuals. They're very explicit.
Matt
Matt Lind
Animator / Technical Director
Softimage certified instructor:
Softimage|3D
Softimage|XSI
speye_21@hotmail.com