Asking which is "better" seems like a false question, a type error.

The "gamble" framing works better. Donating to a short-term charity is equivalent to taking a very-high-probability bet for a comparatively but not absolutely small impact (e.g. distributing malaria nets to prevent malaria infections), which gives your donation moderate expected value (EV). Conversely, long-term charities are more speculative but also more ambitious, so donating to them is like taking a low-probability bet for a comparatively bigger payout (e.g. averting extinction).

From my perspective, if one is sufficiently risk-tolerant, some of the best long-term charities seem to offer better EV than the very best short-term charities. But I've formed that impression by reading about these topics for years, taking some pretty weird argument seriously, etc. And I care about EV rather than certain success, so I'm fine with making long-shot bets that may not pay off. In that sense, I treat donating like I would investing.

In your case, it might help to ask yourself what you expect your donations to achieve, how risk-averse or risk-tolerant you want to be in donating: do you consider a donation more like an investment in some speculative altruistic outcome (which might mean emphasizing EV), or like a purchase of a certain altruistic outcome (which might mean emphasizing high probability)?

If a purchase doesn't pay off, that feels like you've wasted your money; whereas if an investment doesn't pay off, that's just bad luck (assuming your assessment at the time was correct of this investment being high EV).