Jack (Earnest) Worthing is a man approximately in his late 20's or early 30's, presumably an orphan, and the guardian of a niece which is related to the man who adopted him after finding him inside a handbag at Victoria Station.
As it was, his protector was a rich man, and Jack enjoys a home in the country (where his name is Jack) and a place in the city, where he goes to entertain himself under the name "Earnest". His character is quite favorable for marriage based on on his income, but his lack of family history makes it a burden for him to marry his lady love, Gwendolyn.
While Jack seems to be the symbol of decorum, Algernon Moncrief is the epitome of the Victorian Dandy.
Algernon is younger than Earnest. He is an aristocrat living way above his means in London. He is characterized by always being hungry, or eating. He does not have any cares for marriage, family, respectability nor responsibilities. He owes money to several debt collectors, and he is apparently more worried about being fashionable, acquainted and fed than stable. He depends on Earnest for his meals at Willi's and to reach his love interest, Cecily- Jack's niece.
In terms of similarities, you can conclude that Earnest (the character Jack pretends to be when he is in the city) is a mirror image of Algernon. However, Jack himself has also similar traits.
Both Algernon and Jack lead double lives: Algernon escapes to the country to visit a fake invalid friends he named "Bunbury" while Jack escapes to the city under the name of Earnest.
They both share a fascination with hunger and danger- When Jack is Earnest in the city, he too runs humongous bills at restaurants and gets in trouble with creditors. Also, like Algernon, he shares a love for the ladies. In the end we find out that they are actually brothers, and that their father's Christian name was Earnest after all-making them both "dully" Earnests