Both of these have the same aim to make a long wallet address into a easy to remember human readable phrase or name to make sending crypto between people an easier experience.

Should you purchase a domain name for yourself? This is a personal decision, many feel that these are not required and simply using copy paste function or scanning a QR code is sufficient.

I've highlighted some key points in the differences for both ENS and Unstoppable domains below along with links to both websites if you would like to learn more. Both websites have information on supported wallets/Apps and browsers.

ENS

https://ens.domains/

Most widely integrated blockchain naming standard

Pros

• Decentralized
• you can purchase any domain that is available
• Prices are dependent on character limit and not on the name itself - example Kevin.eth would only cost you $5 if available
• domains can't be lost forever
• you can use ENS with DNS names you already own (most DNS names are supported)
• $5 per year + gas fee is the minimum price, makes it accessible to more people
• On Ethereum mainnet

Cons

• you must pay a per year registration fee $5 minimum so for 20 years you are looking at $200 (you can pay for multiple years up front)
• domain squatters will purchase sought after domain names to resell for a profit
• must pay Ethereum gas fees
• you must use a hot wallet with eth to purchase (con for new people I guess)

Unstoppable Domains

https://unstoppabledomains.com/apps

Biggest competitor to ENS

Pros

• one time purchase and you own the NFT for life
• can purchase with credit/debit cards
• easier purchasing experience for new people with no crypto experience
• for corporations or celebrities - names are reserved by unstoppable
• no gas fees (on polygon)

Cons

• centralized - company must make profit to continue to operate
• adds a premium to certain domain names - example: kevin.bitcoin cost $25,000 (premium)
• reserves certain domain names for corporations or celebrities
• domain names start at $40
• domain names will be lost as wallets are lost or owners of domain names die - example: if the owner of Hodl.bitcoin dies or loses their wallet that domain name is lost forever, no one will ever be able to use it again.
• Domain names are on polygon not Ethereum

There are many more points in favor or against both, ultimately you will need to decide if you want to support a decentralized public service or a centralized corporation trying to make a quick buck.

^{Disclaimer: I am biased towards ENS}