Level sync system

[ItMe]

Let's say you que up and you get Wanderer's Palace.
That synchs you to iLVL 110.

The first thing you need to know is that when you iLVL synch you lose any bonuses from materia.
Your piece acts like it has no materia when it is iLVL synched.

As for the stats on a piece itself, let us take a quick look at some iLVL 110 PLD body pieces:

Heavy High Allagan Coat


Noct Lorica


Wootz Cuirass

If you take a look at their main stats (defense and magic defense) you see that they are all 162 (note, the Wootz Curiass can only reach this value if it's High Quality).
If you synch down to iLVL 110 your defense and magic defense will synch to 162.

As for the other stats, they seem a little less uniform, but there is an easy method to it.
Each of these pieces has 4 substats, wether they be strength, vitality, whatever.
But the highest valued substat gives 46 points for all of these pieces (funnily enough, they all give 46 to the same substat: vitality)
That highest value is what ALL of your gear's substats will synch down to.

So if you come in with an iLVL 115 piece like this one:

Mythrite Hauberk of Fending

You can see that, like, some of your stats will be a little higher than the iLVL 110 piece, but only one of them crossed that 46 point threshold and would get capped at 46. And you would lose all bonuses from materia.
That's not great, and that means you're ultimately gaining a little bit of stats from the piece and losing more from the lack of materia. When just running dungeons, alliance raids, etc this is fine. The stat loss is small enough that it really makes no difference in that content. If, however, you are doing a new Ultimate you should be aware of this and try and get gear that is just a little older because whatever is current will always be in this weird zone where the materia is worth more than the tiny stat bump you get from newer gear.

But, if you've adventured for a bit and you go into Wanderer's Palace with an iLVL 185 piece, something that's gonna have a much larger increase over iLVL 110 than iLVL 115 does...
All of your substats will be over 46:

Sky Pirate's Coat of Fending

All of your substats are synching to 46.
That's a huge increase, way larger than what you would have been able to accomplish with materia, and this one of the reasons why doing lower iLVL content (even just within the same expac) can feel much easier.



So to answer your question

I have a 50-lvl sword and a 30-lvl sword. Would wielding a 30-lvl sword make any difference compared to 50-lvl sword, since it's a 20-lvl dungeon anyway? Same goes for armor, of course, and stats they give to character.

In some situations that level 30 sword might be technically better in a very small way, but unless you're doing really cut throat content it's generally unimportant/worse to stick with lower iLVL pieces. Unless you are trying to do something very specific with your stats in the highest end content just get that iLVL as high as you can and you'll have no problem ; )