Well, till date we have discovered the small links and connections that suggest paths are either linear or cyclic, but they are all interconnected here and there. So assuming the 'text-bookish' thought that things are either cyclic or linear is itself a flaw. With new flux and omics tools in place the potential is there to find many connections, but dedications needed from classical one-gene one-protein  one-function studies are presently lacking and hence new discoveries have stopped on pathways or hardly add to our so-called knowledge anymore. Anyways, either cyclic or linear, all should be advantageous for an organism and non-disadvantageous from their perspective at least (or else should not have they been discarded over the evolution/ course of time, say in microbes where evolution is really fast?). "Cyclic is NOT closed" and "linear does NOT mean there are no offshoots or feed-backs or similar regulations"! Good question to ponder and work for sure. Let's talk on this more and let great comments come from real explorers ! Thanks for the question. Best wishes. Biswa

First and foremost, the conventional view about metabolic pathways as linear and cyclical is flawed. That is the way reductionist philosophy wants to understand things by breaking it into comprehensible parts. However, the system's view about metabolism is gaining rapid currency. It is a complex network of metabolic web in which interconversion and allosteric positive & negative regulation dictates the fluxes. For instance, fructose-1,6-bisphosphate, in spite of being part of the "linear" glycolytic chain, is a hub of high intensity interactions spanning several different pathway including nucleic acid synthesis pathway. Another interesting pathway is the extensive bifurcating fluxes emanating from several intermediates of purine metabolism going into TCA cycle, several amino-acid biosynthesis pathways and other metabolites... 

Aside from the interesting perspectives above on biochemical pathways as parts of networks, it seems to me that there are good heuristic reasons for depicting metabolic pathways in particular ways, such as linear, cyclic, or bifurcating. Glycolysis is shown as a linear pathway to demonstrate the sequence of steps leading from a starting point of interest, a single molecule of glucose, to an endpoint of interest, typically 2 molecules of pyruvate. Fatty acid biosynthesis may be shown as circular to emphasize that the same sequence of enzymatic steps is carried out repeatedly as the fatty acid chain grows. Oversimplified from a network perspective though these diagrams may be, they depict important aspects of what actually happens.

This doesn't answer Daniel's original question: what are the advantages/disadvantages of each type of pathway? If there are multiple different ways for a metabolic pathway to evolve, the process of evolution by natural selection will favor the evolution of the pathway that is best-suited to the survival and reproduction of the organism. There are alternative ways that organisms carry out some metabolic pathways, varying either by species, or by tissue, or by cells depending on the availability of nutrients. A classic example is anaerobic v. aerobic respiration, depending on how much oxygen is available.

usually cyclic pathways are a group of compounds, enzymes ,.. serving a continuous production or degradation of a substrate yielding an end product of 2 types at least; one of which splitted as the end target of the pathway and the other re-enter the cylce as a basic unit to start a new cycle i.e. one of the end products is a nessesory starter for the next round, while in comparison to linear pathways the end product(s) is splitted to serve its function in the cell without going back to the pathway (even if feedbak inhibithion or stimulation effect the produced molecule doesnt under go the pathway again). Consequently, I think cyclic pathways take place in the very important, continuous and cross sectional metablic pathways that may employ different tributaries and produce large amounts of their end products (the ring shape can uptake a substrate molecule in any step to end with same starting point with the same starting compounds)

 Actually, most biochemical pathway is some kind of cyclic, depending on growth conditions. Two advantages I can see from cyclic pathway are 1) to recycle substrates otherwise is very costly to synthesized from the beginning and 2) to keep balance the pool of energy carriers like ADP/ATP and the pool of electron carriers like NADH/NAD+.  

For example,  although glycolysis is considered as a series of linear biochemical reactions with final products of pyruvate, ATP and NADH, those reactions can also be viewed as  as a cycle especially under anaerobic conditions. Pyruvate does not go into TCA cycle without enough oxygen. Instead, pyruvate is fermented into lactate (in human) or ethanol and CO2 ( in some microbes). Why? Firstly, because organisms need ATP to survive and when ATP is consumed and it turned into ADP that goes back to glycolysis to synthesize new ATP.

Another thing the pool of NADH?NAD+ . Probably, the cycle is clearer in the balance between NADH/NAD+ during glycolysis. Glycolysis deposit electrons to NAD+ to form NADH.  So this set of  biochemical reactions requires a lot of NAD+ input and could produce a lot of NADH. In that case, NAD+/NADH pool does not balance and it can't go very far if they are not recycled.  However, the fact is that under anaerobic conditions cells can transfer electrons from NADH  to pyruvate and generate lactate or ethanol as final products. By doing that way, NAD+ is regenerated and can be put back into glycolysis. Therefore, by recycling NAD+ and ADP, cells can get ATP continuously from glycolysis to survive, although this results in the accumulation of lactate or ethonol and CO2.  

It should also be noted that the cyclic biochemical reaction in biological systems is not a close cycle but always with at least one substrate input and one or more products output. Therefore, it is more like an open cycle. And those cycles are not perfect cycle. There are often cross links within cycles or among cycles (eg,  urea cycle and TCA cycle).