The difference in one sentence
T-money stores value and deducts eligible fares across Korea. The tourist Climate Card is a time pass for unlimited covered Seoul transport. They are not interchangeable: one maximises coverage, while the other can cap the price of a Seoul-heavy plan.
What changes the answer
The important inputs are paid journey groups per day, distance, days in Seoul and whether any trips use excluded services. Count a connected bus-to-subway trip with a valid transfer as one paid journey group, not two raw taps. Airport buses, the AREX Express, Sinbundang Line, GTX and out-of-range journeys need separate treatment.
The honest comparison
Compare the pass price and physical card with the pay-as-you-go fares you would actually incur. Card purchase costs matter if you do not already own one. A result that ignores excluded rides may make the Climate Card look cheaper than the full trip really is.