I guess it kind of depends on what kind of look I want, and how much work it is to get to that particular colouring medium at the time lol
I love my copics, but have also recently discovered Tombow watercolour markers. I've played a bit with Tim Holtz distress markers and they look pretty great too (oh dear, I was supposed to stop with the Copics!). I find copics amazing for getting that just right coloured in image like I might want in a colouring book, I always thought it would be amazing to be a colourist at Disney and it reminds me of that kind thing. This is an example of the kind of stamp I love with Copics The Stamp Spot: Royal: Some Odd Girl Stamps!
(note: this isn't my work, just a piece I like a lot). Although they take practice and are definitely pricey, I do adore them. If you are going to go with Copics, I would consider ordering a set from Oozak.com or something to start, much cheaper pricing than anywhere in my city anyway. The other great thing I love about Copics is the amount of things you can colour with them, you aren't just limited to card stock. I now have large stacks of white ribbon, flowers, brads and other embellishments, because I can colour them to match my specific need with the copics and I don't have to worry about the colour running of fading, saves me a lot of decision making at the stores! You also have the option of purchasing the airbrush system later on and can get into airbrushing as well.
I use watercolouring (with markers or my ink pad) for a less precise look since I find it not quite as easy to control, although I have seen some truly amazing colouring work done with watercolours. I prefer to use watercolouring with stamps that don't have the clean distinct lines (like Tim Holtz stamps (examples attached)
That being said, I've been having a great time creating different background looks with the watercolours, it's almost hypnotic to just be able to randomly apply colour to the page, swish it around, and just add whatever you like with no lines. For watercolouring I also really like to have the aqua pens (they are filled with water so that it is dispensed in a controled way on to the brush) so that I don't need to sit at the table with a bowl of water, I just fill it up and curl up on the couch with my markers and my watercolour pad and I'm ready to go.
I hope that helps instead of adding more confusion!