a thing which starts annoying me a bit is that even when i initiate a 1h power attack first, if an enemy with the same type of 2h weapon starts his power attack at the same time or slightly after me, he always hits me first...?

As you probably know the weapons have different speeds, AI and yourself have different abilities/skills/perks plus level. I presume all this is what's making the difference.
Maybe you're doing different power attacks to each other and some are faster than others. I don't remember having this issue when I used a 2hd Character.

Edit: i meant 1hd

no i am using a 1h sword - others are using 2h weapons...this is what annoys me especially...maybe it is the kind of power attack but i wouldnt be aware of it

I see now, still, it could be all of these factors, also, armour type makes a big diff too

Use standing power attacks (don't move while doing the power attack), much faster than all the others power attacks types (forward, backwards, side). You can definitely interrupt a 2h power attack with a sword if you're quick and use a standing power attack.

There is a nice left handed sword stab to the gut, very fast and powerful.

One handed attacks are always slower and do more damage then two handed attacks.

...think youre messing the two up...