What makes Brazilian coffee unique compared to coffee from other countries? Can you tell me what makes Brazilian coffee unique?
Brazil is unique in that it is the largest producer of coffee, but it is also unique in that it produces a huge volume of dry processed coffee.  Dry processing is not unheard of, but is much rarer in other countries.

Dry processing produces a coffee that IS different than most other processing methods. The coffee tends to roast differently and also produces much more chaff when roasting.  It also tends to have a different flavor profile than the same coffee processed differently.

Many countries or regions will espouse the benefits of their method of processing, but there are other factors that greatly affect the reasons for choosing a particular method.  High humidity or rainfall areas will generally have a hard time dry processing coffee.  More labor intensive methods may be unfavorable in areas where labor is not had cheaply.  Water intensive methods will be undesirable in frequent drought areas or areas where water is expensive.

Brazil is somewhat synonymous with dry processing.  My roaster has a line on it for "Brazil" coffee.  What it really means is dry processed coffee.  Filling the roaster with dry processed beans past the line will overload the unit's ability to get rid of chaff as fast as it is produced and ruin the roast.  But even in the equipment manufacturers world, the two mean the same thing.