For example, say there is a call option with a strike price of $50 for a stock. Now, say there is another call option for the same stock with a strike price of $50 if the stock price is below $60, but the strike price becomes $55 if the stock price goes above $60. Which of these options would be worth more, directionally speaking?
Jonathon, you seem to be asking about a totally hypothetical contract, where, the strike price magically changes, indeed "GOES UP".
In answer to your hypothetical, in very general terms if a call's strike price is higher then it is "harder to get there" and hence there is "more risk" and hence the "price will be lower".
So very simply, in general terms, the "bid goes down" as the "strike goes up". (Makes no difference if in or out of the money.) You can instantly see this on any option chain, example click https://finance.yahoo.com/quote/AAPL/options/ .
Your phrase "worth more" is meaningless.
(Nothing is "worth" anything in this universe. There's bids and asks and last prices in life's database, and that's it.)
So we now know that (real) 55s would have lower bids than (real) 50s.
Regarding your "magic" "50-becomes-55" contracts.
I would say that, surely, they would be a bit cheaper than real-50s. Because, simply, they might (magically) become 55s, which are, simply cheaper.
As everyone has said, really you could ask this on Mathematics or such.
Maybe you are asking this to increase your general understanding of the basics of options, which is a fine idea. Since I only understand the basics of options, I'm happy to try to explain it clearly :)