It's a tough debate, that goes beyond simply which camera has the 'most accurate' color. It's pretty much a debate between art and science, and the different approaches to photography. Do you shoot for technical perfection in every aspect, emotion and feeling and mood be damned? Or do you shoot to try to capture the vision of the scene as you saw it, with the emotion and feeling it transmitted to you at the time? There are many who pursue 'accurate' white balance, correcting away until white balance hits some measured number or a computer meter tells them it has achieved technical accuracy...and then there are those who want the white balance to look as it did, with whatever temperature and cast the lighting at the time presented to the human eye...that may be drastically off the technical accuracy meter - way too red, yellow or blue...but if that's how it looked, then that's what some folks want to show. Think sunset colors...a white object on the ground during a late sunset is going to look extremely yellow, or orange. 'Corrected' white balance would attempt to make the white object look white...altering all the colors in the scene to remove the yellow/orange color cast that the sun worked so hard to paint across the landscape!
The other factor, and the one you mention with your DSLR vs your P&S, is likely the subtle differences in the way cameras render certain colors by default. Sometimes, even making adjustments to the settings won't exactly balance two different manufacturers' cameras, as they both process colors off the sensor differently, different lenses alter the color, noise reduction algorithms alter the color, etc etc etc. There have long been fans of 'Canon color' or 'Sony color' or 'Olympus color'...folks who either have become familiar and comfortable with the rendered colors each of those manufacturers tend to use, or who just happen to prefer those colors. Fans of one typically dislike the others. Canon has long been slightly cooler, Nikons often less saturated by default, Sonys tend towards warmer colors, Olympus often more saturated and punchy. It could just be that you prefer the warmer rendering of your Sony camera...and adjusting the colors in your Canon don't quite hit the same warmth...though playing with white balance could get you there.
As mentioned, shooting in RAW gives you the greatest latitude to manipulate and alter color and temperature to get the result you like. But trying to achieve 'accurate' color is basically impossible all the time, because there is no singular universal definition of 'accurate'. I have always personally embraced the more artistic version of color and white balance - I want to show what I saw with my eye, color cast, warm or cold, heavy on the yellows or reds...whatever it looked like at the time. Just the way a painter painting a mediterranean sunset scene over the sea would have to use more yellows, reds, and golds in his color palette to portray 'sunset colors' on the white-washed building walls, so do I as a photographer want to capture that same cast.
I've personally always enjoyed the way Sony cameras render colors...though I do tend to tweak the settings a bit (I find some Sony cameras prone to blowing out the red channel in bright light). But I've also shot with Fuji, Canon, and Pentax, and was usually able to get the color and WB where I wanted it, and just a few extra tweaks in post processing if they were off a touch. If you really just find you are unhappy with the colors, or don't want to spend the time post processing or creating workflows to correct it, then it might be worth considering a new camera - notably before you go and invest too much in a lens collection. I'd encourage you after making an investment in a nice DSLR to give it a try, but in the end if you already have and are still unhappy, then it isn't doing you any good to stick with a camera you're not enjoying. If you found the Sony colors in a compact preferable, then it might be worthwhile to take a look at their DSLRs - the A500 and A550 are very nice mid-range DSLRs and pricing is strong right now...and the Sony NEX mirrorless APS-C sensor cameras might be interesting if you want something smaller. I've been quite pleased with my A550, and have no qualms recommending it. Certainly try to handle any cameras you look at and see if you're comfortable with them...there are plenty of solid advanced amateur DSLRs out there that are quite good, in the same class as the T2...just make sure they are comfortable, have the features you want, and check out sample images and user galleries to get some feel for the color.
Sony DSLR-A68 / Sony 18-250mm / Minolta 50mm F1.7 / Tamron 150-600mm / Minolta 300mm F4 APO
Sony A6300 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / FE70-200mm F4 G OSS / FE70-300mm F4.5-5.6 G OSS / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses