Babos played for MTK Hungária, NAC Breda, Feyenoord and NEC.

[1] After his career, Babos started working as a goalkeeper coach for the youth teams of NAC Breda.

In November 2015, he became manager of the Roosendaal amateur club BSC, where his son, Dani, played.

In March 2018, Babos joined NEC, replacing Wilfried Brookhuis, who was hit by an Intracerebral hemorrhage.

[3] On 16 December 2022, Babos was registered to the NAC Breda squad as an emergency backup due to the illness of their three starting goalkeepers.