I understand that the latter is a slightly better quality lens but it's almost twice as expensive. Is it worth it for the extra 50mm, USM and build quality?
The focusing is faster, true. Only you can answer whether it's worth the extra price. As for the build quality, it is not weather sealed so I wouldn't call the build quality that much higher.
The extra 50mm might not matter, as the image quality of full frame lenses when used on crop bodies is typically slightly worse than on full frame. So, a picture taken at 250mm with the 55-250 might be practically as good as a picture taken at 300mm with the 70-300, even with extra cropping.
If you are planning to use the lens only during this safari, and live in an area where renting a lens is an option, consider renting some of the better lenses such as Canon 100-400 or Canon 400 prime. I don't know how large animals you are planning to shoot and how far away. I would pick the Canon 400 prime for small animals like birds and Canon 100-400 for large animals.
Now, of course if you are planning to start shooting wildlife more often, and are not willing to purchase an expensive lens, the 55-250 and 70-300 could be good options. I would add among these also a third-party 100-400 lens such as the Tamron 100-400 lens. Third-party lenses sometimes have compatibility problems (example: my Tamron 100-400 had issues with Canon EOS RP), but often times newer firmware fixes them (example: my Tamron 100-400 with the latest firmware works fine with Canon EOS RP).
My experience with 55-250mm at shooting birds is that I used it all the time at 250 mm. Thus, at least for birds, a 100-400 lens could be a better choice.
A good middle ground could be renting some lens you can afford to purchase should you like it. For example, lens rentals offers Tamron 100-400. The Tamron 100-400, unlike Canon 55-250 or Canon 70-300, is weather sealed. Also, the Tamron 100-400 has a focus limiter unlike Canon 55-250 or Canon 70-300.