HAD BETTER and SHOULD are used to give advice.
• You should put cool water on a burn.
• You had better put cool water on a burn.
• You should brush your teeth three times a day.
• We had better study tonight because the exam is tomorrow morning.
Although both have the meanings, HAD BETTER is stronger because it implies a negative consequence if you don’t follow the advice; “You should do it, or else…”
Compare these sentences:
 We should take a taxi because it is quite a long walk.
 We had better take a taxi because we don’t have much time.
In sentence , it implies “We should take a taxi, or else we’ll be late.”
Another difference is that usually HAD BETTER are not used with questions.
• Should I put cool water on a burn? √
• Had better I put cool water on a burn? x
There is a difference in the negative form as well. You can make a contraction only with the verb should, but not with HAD BETTER.
• You should not put cool water on a burn. = You shouldn’t put cool water on a burn.
• You had better not put cool water on a burn.
To make your advice more polite, use expressions such as “I think…” and “Maybe…”
• You should eat less fatty food. — Maybe you should eat less fatty food.
• You’d better call your mom, she looked very worried. — I think you’d better call your mom, she looked very worried.
“You’d better” or “You better”
You may hear someone say “you better” instead of “you’d better”. However, grammatically, “you’d better” is correct – so use this form.