These two products provide some differing features:

DO Load Balancer:

• Allows you to balance requests between multiple droplets
• All traffic between the load balancer and your droplets is done over the private network where traffic is unmetered
• Provides a fixed $20/month cost
• Built in SSL (LetsEncrypt)
• Does not include a CDN (site is available from a single region)

CloudFlare:

• Provides a CDN (site is available from multiple regions)
• Balances load between servers over the public network
• Built in SSL
• Bills separately from your droplets based on features and # of DNS requests.

Both services provide good features for their price points so you will want to decide which way to go based on which features are most important for your use case.