When you are choosing a fertility clinic, regardless of the treatment you are intending to undergo, the success rates matter. Success rates vary widely from country to country, and from procedure to procedure. Your choice of fertility clinic will ultimately depend on many factors, and rarely simply on the success rates of a given clinic. Cost, availability, insurance coverage, and location are also important factors to take into account. But success rates are not irrelevant. Let's take a look at success rates of fertility clinics in different European countries.
Whatever European country you are in, I would like to recommend that you investigate what government body regulates fertility treatments and individual fertility clinics as one of the first steps of your fertility journey. Every country in the European Union regulates fertility treatment, and most make the figures relating to success rates of individual treatments (IVF, IUI, ICSI) at every clinic readily available to the general public. In England, for instance, the Human Fertility and Embryology Authority (HFEA) has a website with these figures. They do a lot more than tracking fertility clinics of course. See "UK fertility watchdog to scrutinize sperm donor websites?" for a good example of their activities.
Many other EU-member states have similar bodies. The overall success rates of clinics in different European countries vary significantly. Belgium is the country that has most live births after IVF (40 percent!), while the United Kingdom has notoriously poor success rates. If you are able to pay for fertility treatments out of pocket and are willing to travel a bit, there is no reason why you should not be able to choose to head to Belgium for its high success rate, or Slovenia for its relatively high success rate and lower cost compared to some other countries. Most families hoping to get pregnant with the help of a fertility clinic do not have that level of freedom, and end up seeking treatment in their own countries. You can still increase your IVF success chances by looking at the success rates of different clinics near you.