In the USA, nearly all roads have been paved, with the result that there are a lot of cars using them. In rural areas, public transit is practically nonexistent. If you want to see specific scenery, visit national parks, etc. away from cities, your choices are car or bicycle. (OK, walking also for those rare people.) But the cars just take the fun out of bicycling.
In the third world, most roads away from urban areas are dirt, and often single lane. Car numbers are down to often just a few a day. Pubic transit surprisingly often does exist even here, but typically, it's a single bus a day going from villages to the local market town in the morning, and the reverse in the evening. While the tourist industry wants you to believe that renting a car is the only solution, for those who like to bicycle, the much better alternative is to bring your mountain bike and panniers (bike bags). When bicycling you meet friendly local people, and you are not susceptible to be robbed as when using cars (especially in Mexico).
Beautiful mountains, different geology (rock formations), new and delicious foods, new customs, interacting with people and their culture, feeling of freedom in being able to stop where-ever I want (camp if no hotel), ancient ruins, strange plants, exercise and lots of it, feeling as in "Zen and the art of motorcycle maintenance" since I am able to repair and solve all problems as they come up (self sufficiency).
The prime advantage of third world compared to 1st world is that there are so few cars once you're away from large cities and main highways. In addition, unlike 1st world, you can put your bike on any bus (roof, underneath or inside) to get to where you want to ride and thus avoid main highways and less interesting regions. You can also bring your bike on a 2nd or 3rd class train. The conductor will make signs for a bribe, so give him a buck or two. It's well worth it.
I've bicycle toured in Costa Rica, Baja California Sur (Mexico, several trips), the Sierra Madre/Copper Canyon (northern Mexico), the Himalaya and Turkey. Tamer countries I toured (mostly on pavement) were Hungary and New Zealand. Trips lengths vary are between 3 and 8 weeks.
My most memorial trip, in 1992, I bicycled across the Himalaya twice, in a one-month 1200 KM loop, to reach Ladadk and Zanskar, two Tibetan kingdoms captured by the British in the last century, now in India.
For my current phone, email and web site, see akos.us