The classic synthetics vs organic debate. In short form, organics feed the soil and are more interested establishing a good root system and healthy plants. Microbes break down the fertilizer and make the nutrients plant available. Synthetics are plant available only with a little moisture, which is why the turf grows faster, which also makes you mow more frequently.
If crabgrass control was applied, it's probably best to wait until fall to seed. The crabgrass control material inhibits root growth of newly germinated seeds. Do you want to be outside watering the new grass all summer, or spend more time with your gf?