Are there any security risks or advantages/disadvantages to using the simple recovery process vs the advanced on a trezor? Is one better than the other?
The simple recovery leaks the seed words to a keylogger but not their order. The advanced recovery is completely safe against keyloggers (as long as there is no camera pointing to the Trezor screen).
The simple recovery asks for the words in random order. Since the words need to be entered on the computer, a keylogger can see them. An attacker could then try the words in all orders to recover the seed. For the usual seed length of 24 words this is still too computation intensive to be profitable, but for seeds with only 12 words it is possible to find the right order in a day on a normal computer.
The advanced recovery uses a similar method to the PIN matrix entry. It asks for each word (in correct order) by giving nine choices where it is in the alphabet, see this blog post with screenshots. The computer displays nine unlabelled buttons and the Trezor screen shows the meaning of the button. When the user presses a button, the position of the button is sent to the Trezor. A keylogger can only know which button was pressed but since the randomization is done completely inside the Trezor, the keylogger can't know which choice the button corresponds to. Since every word is chosen by exactly the same four questions (three times a 3x3 matrix and then a 2x3 matrix with the remaining candidate words), there is no information about the seed leaked to the computer. The only disadvantage is that it takes more time and is more difficult to use.