There is a big difference. USPS priority mail ships with $50 of insurance and gets delivered in 2-3 business days, whereas USPS first class has no insurance and can take up to six days.
Moreover, at the time when your package exceeds a total weight of 13 ounces (370 grams), or reaches dimensions larger than 12″ long x 8″ wide x 4″ thick, it falls into a rate category which makes priority mail much more expensive than first class.