Hello Kathrin,
I would be disinclined to recommend any poetry competition that is solely Internet-based.
If a fee is required to enter, for instance, and prizes are awarded, it's a kind of virtual pyramid-selling: 100 people pay £5 to enter, the winner wins £50, and the organisers make a healthy profit of £450. All the organisers have to do is pick a few winners out of a hat, post them online, and go off to spend their profits.
If no fees or awards are involved, on the other hand, and the only prize is the pleasure of seeing your poem posted online as a winner, it's unlikely to be a prestigious competition, and so hardly worth winning.
I would be more inclined to recommend competitions organised by trusts and charities, where there's an option of sending a hard copy to a genuine postal address, where the judges are well known poets themselves, and where winners' poems are published in a magazine or anthology.
It's also worth looking up the competition on Wikipedia, etc., to make sure it's genuine (and prestigious) and not a simple scam. If there are entry fees, it's worth finding out how much of the proceeds are awarded in prizes.
The Poetry Society website in the UK may be a good place to start. I don't like their choice of poetry, but their competitions are genuine:
http://www.poetrysociety.org.uk/
You may also be interested in this site, if you don't know it already:
http://www.everypoet.org/pffa/
There is much bad poetry there; but I always think that studying bad poems (i.e. what to avoid) is as useful to a practitioner as studying good poems.
All the best,
MrP