I have been doing research on Project Orion. There was this big expensive canceled NASA program to build armored spaceships that had to be blasted into space by exploding nuclear charges underneath them. I have seen two schools of design in these concepts. Some of these Orion vehicles look like giant tank shells, almost as wide as they are tall. But other designs look noticeably elongated, cigar shaped but still chonky. What are the advantages or disadvantages of either design?
George Dyson (son of Freeman Dyson) wrote a rather nice book on Project Orion, which amongst other things will disabuse you of the notion that this was a well funded and well received project (also it was not a NASA project, and I think it predates NASA. As Dyson tells it, a steel man cover was accidentally blown into space during an underground nuclear bomb test, which gave some people the idea that this might be a feasible way of propelling a space ship).
In any case, according to Dyson the Orion concept was supposed to work by having some propellant being turned into plasma by nuclear charges that were ignited at fixed intervals. For that you need a) a big pusher plate basically to be in the way of the expanding plasma and b) (for a crewed vehicle at last) a shock absorber arrangement that prevents the crew from being turned into goop by being subjected to sudden bursts vast acceleration every half second or so (having bombs explode under your butt is not as such a continuous process. You also would need few more accoutrements such as a very reliable ejector mechanism to place the bombs at the correct place at the correct time, but I'm not sure how much this would influence the shape of the contraption).
As I see it, this gives you basically a big round thing attached to a huge rod that travels up and down (unless a bomb misfires or is ignited at the wrong moment, which will probably make for a very interesting death. Also this is of course a comic book depiction of the shock absorber, but it demonstrates the principle) , which would severely limit your design choices for the rest of the vehicle (not sure if there is really a technical necessity for the pusher plate to be round, but you want it big because it shields the passenger compartment against overspill from the explosion).
Also you need room for bombs, a lot of them. I don't have the book at hand, but if I recall correctly the estimate for the interstellar version was that it would take some 2,4 million nuclear charges in the kiloton range to get to Proxima Centauri within human lifetimes, and that did not include any braking.
Some of the more stumpy designs seem to predate any actual work on the concept. I think we can safely say that any actual flying Project Orion-type spaceship would look rather different that those designs.
There was a "flight model" in the bullet design (not using nuclear charges, but TNT), but as far as I can tell this would not have scaled to anything resembling a real-life spaceship.
Pointless bonus fact: There is an Alastair Reynolds novel that features a Project Orion-Type spacecraft that uses nuclear charges the size of a Coca Cola can. This was probably alluding to the fact (again, according to Dyson's sources, who very well may be telling anecdotes) that the proposed mechanism for the bomb ejection was adapted from a Coca Cola vending machine.
Orion drives want to be large, including large in diameter.
In general, bullet shaped Orions are ambitious military designs (including the one bristling with nuclear missiles, autocannon, and dropships that freaked out JFK) or the earlier, less developed designs, and narrower Orions with stuff strapped all over the outside are NASA or NASA-USAF modular designs meant to be launched with Saturn rockets and then fueled and embarked from orbit.
There was also some development over time with investigation of more modular designs.