Interlingua is a naturalistic, constructed, international auxiliary language. As far as such languages go, Interlingua is nearly the opposite of Esperanto, and the two demonstrate the difference between naturalistic and schematic languages.
The international auxiliary languages are a quixotic group, since they are so inherently riven by contention. Esperanto is a language with a strong utopian and ideological tradition; many of the international auxiliary languages see themselves as a means to an end (world peace, human unity, hope for progress), and this trait may be most highly developed in Esperantism. L.L. Zamenhof was a proponent of religious humanism, and the idea of international auxiliary languages (or Esperanto) as a means for human unity was embraced by Bahá'í and Oomoto (大本), practiced by the founder of aikido. Some Esperantists aim for the "Final Victory", in which Esperanto has become the world's predominant second language.
Esperanto is a quirky language; though its creator, its phonology and orthography were heavily influenced by the Slavic languages, and so isn't as easily written in ASCII. It's reminiscent of the risk of conlanging, to merely relexify one's native language, although Esperanto is clearly more interesting and sophisticated than that. And it's greatest strength (its agglutinative structure, easy formation of new compounds, and reliance on few roots) can be a weakness. I've heard that while Esperanto has a word for "right" (dekstra), the word for left is the similar-sounding maldekstra ("un-right").
Interlingua takes a very different direction, attempting to resolve the differences between its control languages. It does seem in some ways like le latino moderne, if only because it has a very Romantic phonology like Spanish or Italian, and re-borrows many grammatical words and phrases directly from Latin. They're very different philosophies on language creation, which create two different, interesting conlangs.
The purpose of an international auxiliary language doesn't interest me, aside from the novelty of a conlang that it might be possible to communicate to other people with. I think I am more interested in Interlingua, even just as an artistic language, as an easy-to-learn Romance language that remains similar to, but still different from, some of the existing languages of Europe. Like the language of a Mediterranean country that exists only in the imagination. Or the fictional settings of Miyazaki Hayao's films...although Esperanto may actually be used for often for a purpose like that. "Incubus" was a very entertaining movie, in its way.
The UMI has a page to search the Interlingua-English Dictionary, as well as an Interlingua course for English-speakers, Curso de interlingua pro comenciantes anglophone. I also like the Italian version, which has readings of the text in MP3. It's also useful to know Enough Interlingua to Fake It. & it's always interesting to look at the Wikipedia of a language.