I would recommend the Hilton Budapest (though I haven't stayed at the other one) I have stayed at this one 4 times.
Its up on the hill in the Castle area overlooking the city...a bit safer area at night time and many very good restaurants with a couple block walk.
Good club lounge that's open from early morning until 10pm and even includes free liquor. This hotel also has an interesting wine cellar/cave below the property with free tastings.
Bigshaker