I'm using both as well, and they both have their pros and cons. TenantCloud gives you a free landlord / company website, which is nice. (Coincidentally, I was going to post a link to my TenantCloud site, but I just went there and it's down! Oops! Looks like their whole site is down. I submitted a ticket.) Anyway, from your website, prospective tenants can find your current listings and apply online. The problem is, I don't really like their online application, and you can't really edit it. You can add some Yes/No questions, but you can't add any text field questions. I also don't like the prospective tenant's process to complete the application. First they have to create a TenantCloud account, wait for a confirmation email, click on a link in that to confirm, and then start the application. Then, it's just not intuitive for the user to complete.
Then, the real problem is it doesn't include credit checks. Just recently they added background checks, but still no credit checks. So, after filling out the application I'd have to make the prospective tenant go and fill out something else to get a credit check. Too much trouble.
Cozy has a more simple and intuitive application and process, and it includes the credit and background check. So the prospective tenant fills one thing out and you get everything you need. I still have some complaints abut their application. (It has things like employment and rental history marked as "optional," and I can't change that. Hello!?! Those should be required fields, or at least I should have the option of making them required!) Still, it's pretty decent overall.
Cozy has web pages for individual listings, but no "company" or "landlord" website. So, I can't have a single URL to give people or put on my yard signs or business cards so people can see all of my available inventory.
So, I end up using TenantCloud for my main website and Cozy for the application / background / credit checks. The problem is, there is an "Apply Now" button on each listing on the TenantCloud website, which goes to their application, and I can't disable it. So I get some people filling out that application, and then I have to direct send them the Cozy link and apply there.
Basically, if Cozy would provide a company / landlord website, it would be a good one-stop shop. Similarly, if TenantCloud would offer credit checks and improve their application and process, it could also be a good one-stop shop.
As for electronic payments, I'm using QuickBooks. I hear Cozy payments are pretty decent, too, but kind of slow. As @Dale Stevens said, TenantCloud payments just ties in Dwolla or Paypal. I also don't use TenantCloud's accounting features because I use QuickBooks for that, too.