Having used both, Wizzair are worse when it comes to disruption, partly due to fleet size which means they can't send an extra plane to fill in for one thet gets held up elsewhere,and they're certainly not as punctual as Ryanair - hence their delay warranty product.
I flew WAW to LTN twice and the crew were terrible. I won't go into too many specifics but lets just say the crew didn't seem to take the job seriously which could have led to a serious accident because his attentions were focused on a female colleague on one flight, and on the second flight, same guy, turned off the lights half way through the flight so he could get romantic with a different girl without anyone seeing.
Saying that though I've flew with them about six times on other routes and the crew have been fine and had no problems, the seats are quite nice, perhaps a little bit better than Ryanair but therre really is not much in it, but I won't fly WAW to LTN again simply because of the fact the couple of experiences I had were so bad.
The problem (and advantage) that Wizzair have is that they are very well known in Eastern Europe and some parts of central Europe, but in Western Europe, the only people who seemed to have heard of them are migrants who have moved from countries where they are well known, apart from a few exceptions. So I think WAW-BUD they will win that war with Ryanair getting hammered.
As for routes from BUD/WMI to Western Europe or the UK and Ireland? I can see them carrying outbound pax to these countries, and also migrants who have moved to Western Europe, but for incoming tourists to Budapest and Modlin I don't think they will manage a whole lot. Ryanair will be much better in that respect.