When printing with a custom ICC profile, you need to make sure that you disable color correction in the printer driver. By default, the printer performs color correction on its own, and Canon printers tend to oversaturate prints. If you print from Photoshop or Lightroom, make certain that before you actually print, you configure the printer driver correctly each time. Make absolutely certain that the color correction setting is set to "None", then manually select your ICC profile before printing.
That said, glossy papers have a higher dynamic range than matte papers, so images that have a lot of contrast between the brightest and darkest shades will usually have smoother tonal gradations on luster or glossy paper. Glossy, semi-glossy, satin, and luster papers can all cause gloss differential with ink jet printers, particularly with pigment based inks, but even so with dye based inks (like your iP6000D). Print color is based on reflected light and light wave absorption by inks (and to some degree, the paper substrate). There are several factors that affect the color and tone of light reflected by a paper. With glossy papers, particularly bright white glossy papers, there are often whitening and brightening agents included. Optical brighteners are usually most sensitive to UV light, so viewing a glossy and a matte print under indoor tungsten lighting will cause the color rendition to look different. Glossy papers with brighteners will look best when viewed in bright "natural" light, either produced by a bulb that outputs around 5000K with some UV component, or under actual sunlight.
The color of the paper substrate itself will also play a role in how colors look. Glossy papers often tend to be on the cooler side of white, although there are some brands (Moab, Hahnemuhle, etc.) that offer some "natural" white gloss and luster papers. Most matte papers have a more natural white than bright white (although again, high quality third party brands like Moab, Museo, Hahnemuhle, etc. have some bright white matte papers). Natural whites usually range from very warm to natural warm, and will change the look and feel of a print in comparison with bright white glossy or luster papers.
It is important to use the right paper for the job. Papers are by no means equal, and have more differences than just glossy or matte. The "temperature" of the paper itself, the purity of its white, the texture of the paper surface, the use or lack thereof of brighteners, the level and type of gloss, etc. all affect how a resulting print looks. Some things look superb on glossy paper, but lack depth and punch on matte. Some things have fantastic warmth and feeling on matte, but look unrealistic on gloss. You will need to experiment a bit to determine which of your photos look good on gloss, and which look good on matte. You might also want to try a few third-party papers, as they often have FAR more variety than Canon does. Most quality papers, like Hahanemuhle, offer their own custom ICC profiles that ensure correct color reproduction with Canon printers and their papers.
In my own experience, photo rag matte papers are FANTASTIC for landscape photos. They bring a warmth and texture that makes the best of expansive nature scenes. Luster papers, or soft gloss papers, bring out smoother tonal gradations and slightly more dynamic range for portraits. I generally try to avoid papers with optical brighteners, as their color reproduction changes depending on the light the print is viewed in. There are some quality bleached white papers from Museo that offer a middle or neutral white, brighter than the common natural white, that just makes the most stunning black and white prints. I highly recommend looking into Museo, Hahanemuhle, Moab, Ilford, and Breathing Color. Find the tones, weights, and textures that bring out the most in your prints.
As for the question about your particular printer being lower than par for professional prints, yes, it is. That particular printer model is a consumer grade photo printer that is designed more for your average home user who just wants to spit out 4x6 or 5x7 photos of their family, friends, and vacations, or the occasional word or business document. It is not designed as a professional grade photographic printer. The Canon PIXMA Pro 9000 II and 9500 II are Canon's professional grade home photographic printers. The 9000 is a dye based printer, and the 9500 is a pigment based printer. Both of those printers can produce VERY high quality prints up to 13x19" in size. The 9500 is comparable to Epson printers, although it is more tuned to saturated greens, blues, and reds (where as Epsons tend to cater towards more saturated oranges and magentas.) Unless you print a lot of prints with highly saturated magenta, a Canon 9500 or any one of the Canon imagePrograph printers that use Lucia or Lucia II pigment inks will produce the highest quality prints you can get from an ink jet printer these days.