Hungary is an interesting one without doubt but the war at Budapest is not as cut dry as Wizz winning here, despite what some of the Hungarian press seem to think, as having been to Hungary a couple of times since the competition between then and Ryanair started up it's very much a mixed bag.
Whilst Ryanair did pull out of a couple of routes they announced, it is not all one way there, on some routes Ryanair are beating Wizz on loads and on other routes Wizz are beating Ryanair. The more Eastern routes will always be more popular for Wizz are better known here, and indeed Ryanair generally don't compete on a lot of these routes.
However in Italy Wizz are said to be struggling from Budapest and they are pulling out of Bergamo (July) and Forfi (October) because of the fact Ryanair's flights to the same areas have had better take up than that of Wizz. So it's not all one way despite how some of the press like to to portray it. Each company has it's strengths in the European market,
Wizz is not that well known in Western Europe, other than by residents of Eastern European countries who have moved to Western Countries, whist similarly in the likes of Bulgaria, Ukraine, Latvia, Macedonia, Lithuiania, Romania and Serbia without a doubt are Wizz territory and they enjoy very good brand recognition here,whilst then you have Norwegian, very successful in Scandinavia, but again not hugely well known outside here.
Right now at Warsaw and Budapest there is a fare war between Ryanair and Wizzair which means both carriers are selling at crazy prices, Wizzair with 2 Euro fares and Ryanair with 5 Euro fares on routes which are competing with each other, such competition is going to last until a lot of such duplicate routers fail to become duplicates anymore as winners emerge on each route. After that you will see prices go to more sustainable models, something which has bore out time and time again.
Generally outside those two airports, there is not much between the two airlines. Ryanair are without doubt more punctual than Wizzair and are better in times of a crisis because of their huge fleet and have lower fees for the most part along with a better, non fuel surcharging baggage policy. Wizz on the other hand don't have as many announcements during flights which some people prefer.
Personally I use both airlines and generally wouldn't avoid either, but I do generally find the airports that Ryanair use are more convenient for me in Western Europe and on routes where there is no competition, Wizz tend to be quite expensive, compared to routes which Ryanair have no competition, for example routes from Cork to Poland are expensive, lucky to get a flight cheaper than 60-70, From Dublin the highest price I've paid in 5 years with Ryanair is 44.99 and sometimes less. Wizz claim it's because of Government taxes at Cork, yet the tax was reduced to 3 euro but they are still charging 10 euro nearly a year later.