The budapest has a similar problem to the Chigorin defense, even if white doesnt have an outright refutation (say the same way the latvian gambit is busted), white has way to many pleasant lines to claim a larger than average advantage and in a few of the critical lines, black is walking an objectivity tight rope where the reward is just surviving.
What's the problem with the Chigorin?
It is an absolutely sound defence, where white has trouble demonstrating a slight edge, let alone an "outright refutation".
i dont think Chigorin is refuted. Its just a big homework defense where white has many different tries for advantage. I dont think its as sound as say, the 1.e4 nc6 2.d4 d5 Nimzowitsch defense, where only 3.e5 seems like a real try for advantage. Its more like the pirc where white has many acceptable set ups and black must do lots of homework to take a little longer to equalize.
I went through a period where i had to decide between 1.d4 nc6 2.c4 and either 2.d5 or e5 and i found the e5 positions much easier to play despite preferring the d5 nimzowitsch lines to the e5 lines.
and i think both Chigorin and Budapest reflect an innate difference between 1.d4 vs 1.e4 lines. Its that much harder to Spice a game up as black vs d4 so black must take slightly more risk to the objectivity of the position. There is no equivalent to the Sicilian vs d4. All the attempts to really win like the KID, dutch, benoni, and arguably even the Grunfeld carry inherently more risk. The closest one to the asymmetrical but sound nature of the sicilian is probably the nimzo-indian and black cant even force it .
The budapest has a similar problem to the Chigorin defense, even if white doesnt have an outright refutation (say the same way the latvian gambit is busted), white has way to many pleasant lines to claim a larger than average advantage and in a few of the critical lines, black is walking an objectivity tight rope where the reward is just surviving.