The OP started the query re comparative values of investing in Poland or Budapest.
First thing that comes to mind is the attempt to make a compare/contrast evaluation of (a) an entire country against (b) a city in another country.
No reflection on the poster, but this just serves to show how foreign property is sold to irish buyers, or indeed more correctly how irish buyers approach the process. At one point in time the flavour of the month is Budapest, next month it's Bulgaria or Poland. Get my drift? A couple of years ago the perceived wisdom was that buying in Budapest (capital of Hungary, for the uninitiated) was the easy way to riches, and there was a rush to buy there, but often with no thought or strategy. Then the marketing-driven tide turned to Bulgaria, again with no logical approach by buyers. Now "Poland" seems to be the fashion, but again with no research and no logic in most cases -- almost all the available information is coming from marketing companies or second-hand from "a fellow I know down at the pub."
A proper comparison might be more correctly made between Warsaw and Budapest for instance, but nobody buys property in Warsaw it seems, just in "Poland"!
Forgive the deviation from the original question! Just sometimes someone needs to say "stop, hold on, what exactly are you thinking of doing with your money?"
To get back to the question, for my money Budapest wins out over most of the Polish cities (except for parts of Krakow maybe) in terms of potential investment value. Rent returns are reasonable enough, and some good projects give a fair return and seem set to grow in time. The city is well placed strategically and geographically in Europe, better than most Polish cities, and the fiscal rectitude programme of the current government will pay dividends in years to come in my humble view.
It goes without saying though that not all of Budapest makes for good investing, but there are rich enough seams for the canny buyer who knows his cities from his countries!