stock price vs. option price vs. profit gain

The strike price of stock A is 120 dollars and the strike price of stock B is 240 dollars. The expiration date is the same, one month later. Is it better to buy the option of stock A? This is my feeling and I just want to confirm with someone. However, if stock B grows faster, how do I decide which option to buy? Thanks

There are two missing missing puzzle pieces in your equation which contribute to an accurate answer.

1. Both stocks pay no dividend and if they do, the dividend of stock B is twice that of stock A

2. The implied volatility of the options of both stocks is identical and will remain identical throughout your ownership.

If all conditions are met, then it makes no difference which options you buy because option price is linear in regard to price. IOW, the cost of a $240 call on a $200 stock will be exactly twice the cost of a $120 call on a $100 stock. And if they move up the same percent and all conditions remain equal then both options will profit by the same percentage.

The last sentence in your paragraph is problematic. If stock B grows faster (which I interpret to mean that its price rises more percentagewise) then it would be the obvious one to buy.

Which option to buy is a can of worms. You can figure this out with an option pricing formula but it's a bit of grunt work. The path of least resistance is some decent option modeling software that displays graphs.

A really nuanced way to compare two positions in the same stock is to input one option position as long and the other as short. If the positions are equivalent, you'll get a horizontal graph across time and price. If they are not equivalent you'll get a sloping graph and with a bit of further comparison, say expiration values, you'll be able to tell which option leg is better.

Read this answer that I posted earlier today about a similar question. It offers some ideas onhow to determine which option to buy.