Early fall is by far the ideal time to seed, not spring. In the fall, cooler temps help keep the seed moist without water evaporating and competition from weeds is greatly diminished. Also, the new grass has a couple of months to grow in the fall, followed by another few months of desirable weather in spring. This gives the grass time to get established before hot summer weather arrives. It also allows for the use of a std pre-emergent crabgrass control.
Spring is suitable for doing spot repairs, etc., or to establish a new lawn if absolutely necessary, however given a choice, fall is by far better.