Hi - not a very timely reply, but hopefully a useful one from someone who spent a few months in Budapest this summer freelancing/looking for work in consultancy.
First issue is it is becoming very difficult unless you speak hungarian. Second is the market is quite small and tends to focus on Central European trends etc. On that basis the main players are D&T, KPMG and PwC - typically developing a multi country presence. The strategy houses, Mckinsey, Bain etc all have a presence but it only seems to be about 3-4 consultants ie a presence rather than a real operation and as a result limited job opportunities. There are also some system integration houses.
Main sectors and issues are BPR/cost reduction focusing on manufacturing related sectors. This is linked to inward investment and the need to remain competitive. This includes the imminent EU accession.
One final point - unless you get the job from outside Hungary, you will be treated as a local and paid accordingly ie poorly by western standards. Having said all that, its a fab city so good luck
