Plenty of management companies in Budapest; many of them do a reasonable job, there are a few good ones and a few bad ones, just like anywhere else.
Many buyers make the mistake of thinking that a management company is working solely for them, for maybe 10 or 15 percent of a small rent roll. One of the most common conflict scenarios I have seen with small investors is an unrealistic expectation of what a management company can or will do for you. The problem is often compounded by the agressive stance taken by some owners, generally getting on the wrong side of some unfortunate and not too well paid clerk in the management company office.
The reality of renting residential properry is that things go wrong. Tenants don't pay rents on time or default altogether, move out without warning, do damage to apartments, etc. This is as true in Budapest as it is in Ballsbridge. To expect that the rent minus the management charge is your income stream from a property is over-ambitious; in some cases it all goes smoothly, but there are exceptions and these can cause frustration to overseas owners, in particular if they have not enough of a buffer fund to cover repairs etc.
The best way to manage a management company, in any city, is to be proactive. Get to know the person dealing with your account. Bring them a bottle of baileys or a few chocolates when you visit, and put them on your funny email list if they are receptive to that. Get to kmow them, and understand that they have a hundred more owners who also have problems, often all at the same time.
Whenever I look at situations where there is open hostility between a management company and an owner, it is a sure bet that both sides are somewhat to blame. Failure by owners to answer emails, to put the MC in funds when a bill has to be paid, etc etc; these are all part of the landscape where management companies are concerned.
In the area of rental property, you have to be able to handle the heat if you want to stay in the kitchen. In your case, if you are already set in your mind that this business is not for you, you are probably better off getting out and staying out, for the sake of your sanity.
In my long years dealing with such companies I have found that the human approach is the best. I make it my business to be on first name terms with the staff in the various offices. I have many of their birthdays on my phone calender, and I send them a text or an email on the day. I give them a small gift when I am in town, or take them out to lunch. I give them a card and a voucher for the local department store at Christmas. I still have the odd problem, but nothing that concerns or worries me.
If you still want to stick out this business, and it is not for everybody, then don't run away at the first sign of a problem. Deal with it, don't let it fester. Contact Budapest on this board with a pm and ask his assistance; many posters have told me that he knows his job. But lose the defeatist posture first!