Currently I am using Nikon d3200, and I am thinking to upgrade my camera to Canon 600D/ Rebel T3i. Is it a better idea to upgrade from Nikon to Canon. Though I can spend on some new lens for my Nikon, I've read that Canon has some built-in color enhancement also does Canon 600D have any drawbacks. please advice.
Since you should shoot in raw this color enhancement stuff is more or less pointless. It just look better on cam screen on location, but on the computer at home the raw files look nearly the same.
Also the Canon 600D is older as the Nikon D3200, so it would be also not become better.
So some suggestions:
If you shoot mainly in good light conditions and you have actual no problems with ISO performance: Buy new lenses or other equip you might think will help you. Btw. in most cases a good lens (with not so good body) worth more than a good body (and a not so good lens)
If you have problems with low light, ISO and noise: go for way newer and better cameras. If you have the money e.g. Nikon D7500/D500
If you have no problems with Nikon and you are happy with it: Go for the Nikon D5000 (D5200/D5300/...) series or the D7000(D7100/D7200/...) series.
If you shoot mainly with other photographers: Stay or switch the system to theirs brand. Then it is easier to play/work together. (If they agree that you play/work with their stuff.)
Maybe there is a camera rent service by your location: try to rent different stuff and see what will the best for you
As others pointed out, there are a lot of subjective things here. But let's look at numbers and specification:
Measurements by DXOmark shows that 600D is worse than D3200 for essentially all metrics. Not really a Nikon Vs Canon debate, but just that the D3200 is a bit newer than the 600D.
You're considering a downgrade here, not an upgrade.
Warning: Canon user here.
Canon? Nikon? Both brands have good cameras, and for a given price point which brand has the best one changes over time (and depends on specific user requirements).
You eventually get married to one brand, if only because you are used to the menus. But most people invest in additional gear: lenses, flashes, and all things that work with one brand and not the other, and very soon you have spent more money on that than on the camera body (and these things don't get out of style as fast as camera bodies), so brand-switching becomes very expensive.
So you have to think about the medium/long term: what you will do with the camera, what kind of lenses you think you will use and if there is a sufficient choice for either mount (and not just brand, because you can get lenses or flashes from other manufacturers).
Personally I went with Canon some years ago because it looked more hackable and has a greater choice it prime teles (though I still don't own any yet:).
Both Canon and Nikon make DSLR systems today that are not obsolete. I calculated that where I live, today, a good starter kit with 4 cheap lenses for Canon costs 1080 EUR and for Nikon costs 1550 EUR (although you could make these figures anything depending on which kind of lens set you're considering, so some Nikon fanboy could make Nikon look cheaper). If you already have some amount of Nikon equipment, a new body costs perhaps 500-600 EUR whereas for Canon you'd have to buy an entire system for 1080 EUR.
Now, I understand these figures will become obsolete very quickly, but they illustrate the main point that systems are expensive, costing more than bodies do, and thus it doesn't make sense to switch to another system. So, the main point will stand the test of time.
Nikon may be slightly better in terms of noise performance as it uses Sony Exmor sensors (although there may be arguments against Exmor sensors), and because it has 1.5x crop instead of 1.6x like Canon does. So, I would say there is at least a partial valid reason for slightly higher price of Nikon. Also, Canon has a better selection of really cheap DSLR cameras, so I perhaps wasn't comparing apples to apples in the 1080 EUR vs 1550 EUR comparison.
Now, if you only have a Nikon DSLR with the kit zoom lens and no other lens, and there's a valid reason for needing a new body, you could consider purchasing a Canon body. But, in this very specific situation, I would say you would be 99% certainly better off by buying some good additional lens for your Nikon system rather than switching to Canon. Almost always, it's a better idea to purchase a new lens rather than purchasing a new body. Or a tripod. Or a flash. Also, as the others pointed out, 600D isn't an "upgrade" compared to D3200.
About the only reason when it makes sense to switch to another system is if the system has become obsolete and you don't want to spend your time hunting for used equipment. The main non-obsolete DSLR systems today are Nikon and Canon, although there are some non-obsolete mirrorless systems as well (but they are not DSLR as they lack the "reflex" part of DSLR).
You have selected your system, now it's time to stick with it.
Oh, and about the color enhancement: both Canon and Nikon use Bayer filters to capture color. I don't think there's any difference in the hardware. There may be difference in the software. I would suggest shooting raw and using RawTherapee (or darktable if you don't mind it's slightly worse noise removal options). There's plenty of color enhancement options in the post-processing stage.
Learn to use what you have properly! Once you have mastered all the details of your current equipment, you would truly understand if you're equipment-limited or not. More specifically, you would understand why Canon isn't "better" than Nikon.