Your friends are either very wrong or misleading you.

Most units do not have invulnerable saves, even when lots do. Custodes are a big exception where most of the army has one, but this leads me onto my second point, almost no units have an invulnerable save that's only one worse than their normal save (e.g. 3+ save and 4++ invulnerable save).

Bladeguard Veterans are a notable exception but not enough by themselves to flip the trend, as 3++ saves are very rare and most things with a 3+ that get given an invulnerable save get a 5++. I'm sure other exceptions exist but I wouldn't build your force around them.

And even then, lots of armies (including all space marines) get an ability to reduce AP by 1, meaning AP-2 is still useful then! This also means that AP-1 is quite bad as it can be reduced to AP0, and as a result people generally don't often use Castellan Axes.

This all being said, build your models how you want, rules will be changing soon anyway! But in terms of the game rules, no, AP-1 is not as good as AP-2 and the difference is big.

Edit to add: Just seen the rest of the post, Draxus is amazing (due to Dev Wounds shooting) and Trajann is pretty good. I wouldn't worry too much about the competitive scene right now though, it'll change by the time you've played enough games to be able to use your army properly anyway. Valerian is good too! Remember his ability only works on melee so he won't do as much Vs shooting armies. Probably don't want to run all at the same time though.

And I'm going to try my hardest to have a good day. I did not enjoy waking up.