Ternary and Fibonacci searches are two interesting methods for finding information in big data sets, but they each have their own unique features.

Ternary Search:

• This method splits the data into three sections instead of just two. So, it can sometimes work faster than the binary search.

• The time it takes to search is $O(\log_3 n)$. This means it slowly narrows down the area you need to check.

• But, because it has to calculate two midpoints, it can actually be slower when dealing with really large arrays.

Fibonacci Search:

• This method uses Fibonacci numbers to help divide the data. This helps to avoid some division calculations, which makes it quicker when you have a lot of data.

• It also has a time complexity of $O(\log_n)$, but it can perform better when how you access memory is really important.

In summary, both searches do a good job, but the Fibonacci search might be faster for large amounts of data because it has fewer math calculations!