If you travel alone, you have to learn the language of the country. Otherwise, your trip would be very difficult. Speaking the national language makes many things, like shopping and interacting with native people, much more easier. If you travel with a companion, you are possibly not anxious to learn the national language because your friend might already be able to speak this language.
Speaking the national language enables you to get to know new cultures and customs, too. You might see strange customs, but on the other hand, you will understand them because you get familiar with the background of the people. If you travel with a friend, you might be not as open for new things as you are when you travel alone.
Last but not least, you have the opportunity to get to know new friends when you travel alone. Interacting with other people is always the first step to find new friends and you might find someone, who accompanys you for a part of your trip. If you travel with a companion, there is no need to find new friends because you already have one.
Altogether, I am sure that I prefer to travel alone. I would have more opportunities to get to know the language, the customs and the people of the country. As a result, I have the chance to experience a lot of new things.