Hello, as a singer-songwriter major myself, I think I can help. The profession of a "Troubadour" started in the late 1000's and lasted through the mid 1300's. Troubadours were different from the classical artist, in the sense that they were highly lyrical and poetic, rather than being focused on the composition of the music itself. They were very melodic and most were metaphysical/intellectual. They sang about love, loss, and even some humorous/vulgar stuff. Near the peak of their prevalence, there was even the option to go to school to be a Troubadour.
Like the troubadour, a singer-songwriter is less classical in their music. It is hard, no doubt, to get into school to major in that field with out some understanding of music theory and composition. Usually singer songwriters play one or more instruments to accompany them, but some just have others play for them. Most songs written in modern days, deal with the same stuff that the troubadours went through: death, loss, love, and life.
I would say that they are most similar in the way that they seek creativity and how they use music as an outlet. Another similarity is that not many troubadours were respected in their profession, and from experience I know that this mentality is the same today; being a musician is not looked at seriously in the business world. The biggest difference, I would assume, is the resources. The troubadours mainly played on the streets and they might have gotten gigs, but not likely. Now, we have bars, and people who want musicians to come play. It is also much easier to get your music out there now, thanks to social media and iTunes.
I hope I could be of help! I go to a preforming arts school, and I gig weekly at a bar called "The Carousel Lounge" in Austin, Texas!