05 and early 06 had a engine issue. I have a later 06 GT650 and its the same bike form 06 late tell 09 when they added EFI.
As for 250, never heard much issues at all
But yes I OWN a hyosung, got a gt650 06 last year from motorcycle city who had a demo one. 4250$ with warrenty , sv650 second...