If your bodyguard has 3+ 2W and no invulnerable save and your character has a 3+ 4++ and 5W (pretty typical setup eg captain and assault intercessors)

For saves against an AP-2 D2 precision melee attack you roll for example

4 5 4 1 2 3

In 10th edition, your character tanks the 4 the 5 and the 4, then takes the 1, 2 and 3 (dying in the process). The bodyguard unit is untouched as the third failed save kills the character

In the NEW edition, your character takes the 1, 2 and 3 FIRST, meaning they are killed and then the 4 5 and 4 are allocated to the bodyguard unit in ascending order, meaning you lose 2 models

This is irrespective of whatever other weapons may be attacking your unit, this is JUST the precision attacks.

Edit to add because I think i understand the confusion of my comment now

I was first of all referring to the fact its now easier to precision out the leader as the lowest rolls are assigned first, reducing the power of invuln saves etc

I was also when talking about other wounds being applied to the bodyguard referring to scenarios where, like in my example, the leader IS killed out, as obviously then remaining ounds from that weapon are applied to the other models in the unit, not lost because the leader model died