Reliability comes from the fact that in Sanger sequencing (AFAIK) the synthesis of the new strand to the template and the actual reading of the sequence is separated. As you may know Sanger seq uses capillary gel elfo. thus separating the newly produced DNA fragments on a single nucleotide difference, and the reading is done by fluorescence detectors (then base calling etc.) Now compared to this the other sequencing methods like Illumina and 454 detect each nucleotide incorporation that may produce less reliable signals. For eg. in Illumina colonies may overlap on the plate, or in 454 incorporation of multiple nucleotides at homopolymer regions cause a hard time deciding how many nucleotides have actually incorporated. Also it must be noted that quality of the singals / reads is not constant through out Sanger sequencing. The beginning and the end of the reads tend to have noisy and low quality signals, thus actually only the 100-500(-600)bp segment of the whole fragment can be read reliably. Also ABI's SOLID uses a 2 color color-space and each base is read twice and is extremely reliable (99.96% is said by the inventors). Also clever base calling and error correction algorithms may improve accuracy.
It is noteworthy to say that next gen sequencers also achieve high accuracy by taking advantage of their immerse throughput / output - due to clonal amplification of template sequences each original fragment is sequenced multiple times and errors in a single read can be corrected by the use of others.