Both translate as burp or belch. Although each might have other connotations as well, I am only interested in the Spanish for a burp. What's the difference and if it's just dialectical, which one of the two is preferred in your country (I am more keen on Latin America or Mexico)?
The difference is merely dialectical. I have used both and I have never inferred any nuance concerning odour. "Regüeldo" is much less frequent (although in my homeland, Zaragoza, Aragón is preferred although Aragonese Spanish has a knack for expletives) and, according to Cervantes through his most celebrated character, Don Quixote, much more offensive to the ear and, thus, condemned to be ostracized. Five centuries later, it joyfully survives at least in some regions. If you want to sound polite, always use "eructo". If you use "regüeldo", people will probably think you're the kind of person who indulges in and even enjoys the action itself.