I have noticed that there's a huge difference(in sound) between flat and round wound strings.

How are they winded so that they will sound so differenaly?
Oh well, they are completely different!

The Flatwounds ( also known as Flats, Chromes or Boomers) are silky to the touch because the wire wrapping is square in section. They deliver a deep, big bass sound.
They do not have any crystalline or metallic edge as the rounds. They are perfectly fit for some musical genres as blues or jazz,since they were thougth as a substitute string from the uprite bass on the electrical bass. They are used mostly on fretless basses nowadays, because being flat do not ever scallop the fretboard.

The Roundwounds on the other hand have a round ( from which the name) wire wrapping, so they are much different to the touch. They are the strings for rock , punk, metal, and for any music genre where a sharp, definite sound is necessary.
They usually come in two tipes: steel and nickel.
The steel ones last longer but are quite hard either to the touch or the sound, the nickels are smoother and warmer. Most bass players use roundwounds nickels I guess ( I do , too).

If you ask for a brand, I love either the D'Addario XL or the Ernie Ball Slinky.
I hope that was useful.