Making your own songs is much more fun than making remixes I think. Much more rewarding also. Generally I don't like covers or remixes at all. Often they're simply not as good as the original, because a song has to be good to begin with before anyone would want to remix it, and the remixers aren't always that good themselves. But even when a remix is actually good on its own, you're still like "Yeah, but they didn't actually invent this song, which is halve the work. Liking this is betraying the 'original' song.". I seldomly think a remix is an improvement. If the remix get more famous than the original, I just feel sad for the creators of the original for missing their chance to shine. But then again, the original may get better publicity, because people who like the remix may still want to hear what the original sounds like.
Having said that making remixes can have some benefits. First of, it's usually only halve the amount of work it is to create an original song. It's fun to play around with songs you like and do something totally different with it. Or make something comedic or entirely different with a song you don't like at all can be fun too.
I make a lot remakes of old video game songs. I change as little as I can to stay true to the original. Al I want to do is find out how those songs could sound if they were made with more advanced equipment (better sounding samples, effects, mixing and mastering), and more lively sequencing (more different velocity levels, tone lengths, tempo, fades, modulation, pitch bends, etc). This is a little too easy almost, but fun to do, and you get a lot of appreciation, especially on youtube. Also you learn a lot about mixing and mastering this way, in a very quick tempo. Sometimes I totally change the mood of the song, or add instruments I felt were missing from the original.
These remakes I call arrangements, which is kind of a pretentious word, but it's more accurate than remix. Technically a remix is when you use the original tracks that were recorded, and you re-do the mixing process. Generally when people say remix, they don't use the original tracks, but just the melody or lyrics. That should actually be called a cover or remake or whatever.