What is the difference between SOLiD, 454, and Illumina next-gen sequencing?
Here is a short summary of the sequencing technologies you listed. Illumina is the most frequently used one.

Roche/454 FLX Pyrosequencer technology is based on pyrosequencing method, which utilizes the use of the enzymes ATP sulfurylase and luciferase. After the incorporation of each nucleotide by DNA polymerase, a pyrophosphate is released, which further takes part in downstream light-producing reactions. The amount of light is proportional to the incorporated number of nucleotides. The DNA is fragmented and adapters are ligated at both ends. The fragments are mixed with agarose beads, which carry adapters complementary to the library adapters, and thus each bead is associated with a unique DNA fragment. The beads and DNA fragments are isolated in individual micelles, where emulsion PCR takes place and million copies of the single fragments are amplified  onto the surface of each bead. Each bead is placed in a well of picotiter plate (PTP), as the wells have dimensions such that only one bead can fit per well. Enzymes are added to the beads and pure nucleotide solutions are added with an immediate imaging step. On one side of the array a CCD (charge-optic device) camera records the light emitted from each bead. The first four nucleotides (TCGA) are the same as the start of the adapter, which allows for the emitted light to be calibrated according to the type of nucleotide added. The major disadvantage of this method is the misinterpretation of homopolymers (consecutive nucleotides, e.g. AAA or CCC). Such areas are prone to insertions or deletions, as the length of the stretch can be inferred only by the intensity of the light emitted. On the other hand, substitution errors are very unlikely. The 454 FLX instrument generates ~400 000 reads per instrument-run, as the reads are 200-400bp. The greatest advantage of this platform is the read length, which is the longest of all second generation technologies. Although sequencing on 454 platform is more expensive than sequencing on Illumina platform (40USD per Mega base versus 2USD per Mega base), it could still be the best choice for de novo assembly or metagenomics applications. (Mardis, E., 2008, Shendure, J. and Ji, H., 2008).

Illumina is the most frequently used one. The DNA to be sequenced is fragmented into about 200 base strands. Adapters are ligated onto the ends of the fragments and one of these adapters is hybridized on a flow cell. Illumina essentially utilizes a unique "bridged" amplification reaction that occurs on the surface of the flow cell. Localized PCR reaction is performed, and each of the hybridized pieces of DNA will get locally amplified to generate clusters which will have the exact same molecule. Subsequently, the DNA sequence is determined by adding a primer on one of the ends of the molecule. A mixture of modified nucleotides is added. Each one of them carries a base-specific fluorescent label attached to it. Also, each one has the 3' OH group blocked which ensures the incorporation of one nucleotide at a time.  The flow cell is placed under a microscope and when light is shined on its fluorescence, the emission light shows which base was incorporated on each one of those clusters. The Illumina read length is approximately 35 bases, but over billion reads are generated at a time. The major error type is substitution, rather than deletion or insertion (Mardis, E., 2008, Shendure, J. and Ji, H., 2008).

The SOLiD platform utilizes the use of DNA fragmented library, which is flanked by ligated adapters. The fragments are attached to small paramagnetic beads and emulsion PCR is performed to amplify the fragments. In contrast to the other sequencing platforms, sequencing by synthesis is performed by utilizing DNA ligase, rather than polymerase. Each cycle of sequencing involves the ligation of a degenerate population of fluorescently labeled universal octamer primers. A specific position of the octamer (e.g., base 5) carries a fluorescent label. After ligation, images are acquired in four channels, followed by cleavage of the octamer between positions 5 and 6, removing the fluorescent label. After several rounds of octamer ligation, which enable sequencing of every 5th base (e.g., bases 5, 10, 15, and 20), the extended primer is denatured. Different primers can be used to examine the previous or next positions (e.g., base 3 or 6).  The platform can use primers which carry two adjacent correlated with label bases. This approach involves the examination of the bases twice in a cycle, which decreases the error rates. SOLiD read lengths are 25-35 bp, and each sequencing run yields 2–4 Gb of DNA sequence data (Mardis, E., 2008, Shendure, J. and Ji, H., 2008).

References:


Mardis, E., Next generation DNA sequencing methods. Ann. Rev. Genomics Hum. Genet, 9: 387-402 (2008). DOI 10.1146/annurev.genom.9.081307.164359
Shendure, J. and Ji, H., Next-generation DNA sequencing. Nat. Biotechnol., 26: 1135-1145 (2008). DOI 10.1038/nbt1486