I disagree with some previous responses calling one camera or the other "better". Frankly, they are both extremely capable and would be significant upgrades for you, coming from older models that you're now using. The D5600 and T7i themselves are probably more similar than they are different. What might be a bigger consideration are the systems and corporations behind each camera.

The problem with asking a "Nikon versus Canon" question on a forum such as this is that you'll get fanboyz and fangirlz weighing in favoring whatever brand THEY chose.... whether that's "right" or "best" for you or not.

I am unabashedly a Canon user and fan... have used their modern system for 15 years, would probably choose Canon again today if I were just starting out and have no plans to change systems in the future. I like the feel, ergonomics, control layout and menus of Canon cameras better... though I'm sure with practice I could be just as comfortable with Nikon gear.

Canon T7i can fully use and is completely compatible with any and all EF and EF-S lenses produced the last 30 years. You can't say the same with Nikon D5600. With all D5000 and D3000 series cameras, if you want autofocus you are somewhat limited to AF-S and AF-P lenses that have in-lens focus drive motors. That actually includes the majority of Nikon lenses now because they've been gradually converting their lenses to those types. But Nikon has in the past made a lot and still makes some lenses that don't have a built-in motor, that rely upon one built into the camera body to autofocus. (This includes some third party lenses... such as the early Tokina 11-16mm and 12-24mm, as well as the current Tokina 100mm macro lens.... which in the Nikon version don't have an in-lens motor and can only autofocus on D7000 and higher models.)

The Nikon camera can use many vintage, pre-autofocus Nikon lenses. The Nikon F-mount bayonet has been in continuous use since 1959. Canon changed their mount in the late 1980s and essentially "orphaned" their earlier lenses... HOWEVER, via adapters modern Canon can use Nikon (and other mount) vintage lenses quite well. So, if you happen to have any vintage, pre-autofocus Nikon mount lenses, they can be used pretty equally well on both cameras. But if you have vintage Pentax, Leica R, Olympus or several others, they can be used on Canon, but not on the Nikon.

Because of the above, it might be a consideration what lenses you have for each system now. If you were hoping to use them but they need to be replaced along with the camera, lenses can add a whole lot to the overall cost.

There's no disputing the potential quality of either system. Both offer deep, well-developed systems. Be sure to look beyond the initial purchase at other items you might want or need, now or in the future. Aside from the initial "bundles", where Nikon often is a few dollars cheaper, I think you'll find with many comparable items that Nikon tend to be more expensive. For example, Canon EF 70-200mm f/2.8 IS USM II lens costs about $2000.... While the Nikkor 70-200mm f/2.8G FX VR FL costs around $2800. Or, Canon has two popular and very good ultrawide zooms for APS-C crop cameras such as the T7i.... an EF-S 10-22mm f/3.5-5.6 USM for $600 and more recently a budget EF-S 10-18mm f/4.5-5.6 IS STM ($280). The most comparable Nikkor AF-S 10-24mm f/3.5-4.5G DX and AF-S 12-24mm f/4G IF-ED DX respectively sell for $800 and $1150! Nikon has very recently announced a new, budget Nikkor AF-P 10-20mm f/4.5-5.6G VR DX that's not yet in stores and will sell for $307 when it arrives. Or, look at the system flashes: Canon 600EX II "RT" is currently selling for $480... while the most comparable Nikon SB-5000 AF Speedlight costs nearly $600. You can find numerous other examples comparing the systems, some with less and others with greater difference.... But usually the Nikon gear is more expensive.

There also are some differences in support services. In general, Canon factory service and repair dept. gets very high marks and lots of mostly positive reviews. Nikon... not so much. Several years ago Nikon USA implemented a policy where they will only sell most replacement parts to their own network of authorized repair facilities... limiting your choices to about 20. Canon freely sells spare parts to any and all repairers.... which probably number in the hundreds or thousands when you include all independents. There is now sort of an underground black market of Nikon repair parts, recycling used items and distributing third party-manufactured clones of some parts, but even with that it can be difficult to have repairs done outside of Nikon's tightly held network. Purportedly Nikon implemented this policy to assure quality repairs.... but one can't help but wonder if the more monopolistic approach also allows them to control and dictate repair charges and replacement part prices. With the very high reliability of today's cameras, lenses and accessories... this might not be any concern to most buyers.

Finally, Canon is a much larger corporation. Nikon's 2015 gross sales worldwide were about 860 billion yen.... but Canon's were 4X greater at 3.8 trillion yen. Also in 2015, Canon employed slightly more than 190,000 people world.... while Nikon employed about 25,400. In fact, more recent financial reports suggest that Nikon is having some difficulties and some of their divisions are struggling. There are several news stories about this online, some even rumor that the Japanese government might intervene and has discussed some sort of assistance from Fujifilm (at 2.5 trillion yen, also a much larger corp. than Nikon). Canon's larger and more diverse company has weathered various recent photo market changes a bit better and they've been able to maintained their #1 market position, in spite of seeing somewhat slower sales and profits reduced in certain divisions.

If all the reports are true, hopefully Nikon will recover well and be able to continue offering high quality products well into the future. I'm pretty confident they will, but right now I have a little more faith in Canon's ability to doing so. However, Canon users like me benefit a lot from the competition between these companies, as well as from Sony, Pentax, Olympus and all the other manufacturers of photography gear.

In the end, you're actually pretty unlikely to ever see any problems or issues I've mentioned. I know plenty of folks quite happy with both Canon and Nikon (or other) gear and am sure you would have the potential to make great photos either system... and that's what really counts. Go check out the cameras in a store... or flip a coin!

Oh, and beware of "bundles". They can be a good deal... especially "manufacturer" or "major retailer" (B&H, Adorama and a few others) bundles.

But they also can be a rip off. For example, I often see Canon EF 75-300mm lens (non-IS, non-USM verison) offered in bundles... and I'd avoid that particular lens. The EF-S 55-250mm IS STM is only a little more expensive and is a MUCH better lens in many ways. Possibly even better are one of several EF 70-300mm IS USM models, although of course they cost more.

Another example, I noticed a Canon 80D two-lens bundle at Costco had substituted a less expensive EF-S 18-55mm IS STM lens for the better, 2X to 4X faster focusing EF-S 18-135mm IS USM lens that's more typically sold in kit with that camera. Buyers might never realize the difference.... Think they were getting a great deal, although actually they're getting a much cheaper lens.

If I remeber right the 3XXX and 5XXX cameras will not meter with the older Nikon MF lenses. Also if your lenses date to your camera they also will not auto focus.
Yes 30 years ago Canon went 21st century and yes orphaned old lenses. This is no issue to the OP seeing as they do not own any of these lenses and would likely have no desire to purchase one. But unlike Nikon all Canon EF and EFs lenses ever made will work perfectly and 100% of the features are functional on the newest Canon cameras. No one else can make that claim for their lens compatibility Yes Nikon mount but no meter or AF why waste your time upgrading your camera to use old lenses that cannot utilize the features in the camera? There are some in this forum who like to punish themselves doing this and wear it as a badge of honor. That is fine but I would not base my purchase on such a silly premises. Canon is 21st Century in all aspects, Nikon stuck with mid 20th century technology. That is why Canon won the Pro war hands down as you can see at all the major events covered by pros who wanted the fastest, best and most technologically advanced complete system.