Can a wrist sprain be worse to recover from than a fracture?

Sometimes. Most wrist fractures can be treated with cast immobilizaton and will typically heal in about 6 weeks. Sometimes with a sprain one can develop different types of carpal instability which can lead to long term problems like arthritic changes. Swelling and pain. So sometimes a sprain can be worse in the long run than a fracture.
Yes. . Most fractures heal strong enough for return of activities within 4-8 weeks. Bad sprains can take 3-6 months.