John Palmer says
Deeper grainbeds have more uniform rinsing, all else being equal.
An more uniform rinsing can mean increased yield, so then shape does have some impact. As Denny says, taller is better since there is more chance for the water to rinse the grains when fly sparging. (But, up to a point, if the grain bed is very deep then it might become compacted, which leads to stuck sparge or increased channeling further down the grain bed.)
Previously, I used a 70qt cooler for 5 and 10 gallon batches, batch sparged, and typically got 65% extraction, and usually 70% for 10 gallon batches. I'm now using a blichmann 20 gallon kettle and false bottom, and got 90%-92% on each of 10 brews so far.
I don't think the change in efficiency is entirely due to the shape, but I always felt the cooler was far too large for the batch size, making it difficult to get an even temperature. As well as the different MLT shape, the improvement in extraction is probably also due to these other changes in brewing process:
- using a pump to recirculate the mash (more even temperature and enzyme distribution)
- using a precisely engineered false bottom - my cooler had a hand made manifold of CPVC pipe...not quite precision engineering! (reduced channeling)
- close monitoring and adjustment of the pH level of the mash (increased enzyme activity)
- mashing out - more efficient lautering
I'm not adding fly sparging to this list because I really don't know if that improves efficiency - I've not done a batch sparge to directly compare. Will batch sparge the next brew and I'll update this answer with the result.