That is a tough one to compare. I commend you on taking on this task as many of us would be
really interested to find out the pros and cons before voting with our wallet.
Problem. Most people only has one of three.
Reasons. 1. These are expensive apps. 2. Each app has its own desktop server. It would not make sense to install multiple servers unless there is some compelling reason to do so.
Once you have purchased one, you are invested in that system and would be hard pressed to spring for another "redundant" app.
I use LogMeIn and Splashtop Remote (iOS and Mac clients for both) to access Mac and PC. I have tried TeamViewer in the past. I also use Citrix Receiver (connect to hospitals remotely) and RDP apps (connect to Windows server).
LogMeIn is probably the most reliable in terms of connecting from anywhere. It has been out for the longest and I have installed in many PC's across different continents so I can provide tech support for my family. I would prefer a native Mac app rather than web app but the Safari web app works fine. I have Ignition and I find it easy to use on the iPad. I can log in and out of Windows and it hides the remote window. It is my go to app to access Windows PC (non-server).
Splashtop Remote is cheaper and does video streaming (works well local wifi). It is my backup app. Essentially I am waiting for the platform to mature further with updates. A lot of times I have to connect with LogMeIn first before Splashtop Remote would work. It is not reliable for me. It does have a native Mac app but I have trouble with command-tab to switch apps remotely. (Mac to Mac)
Both Rene and Federico praises Screens VNC highly over and over. I am definitely interested but the pricing is a barrier for me, especially now after the price hike. (iOS + Mac = $$$) If I can somehow get a promo code for Mac version, I would not hesitate to buy the iOS version or vice versa. I am a collector of sorts.
What I like to see compared in decreasing importance.
1.Reliability to connect remotely. Can you log out of remote PC (switch PC users) and still connect?
2. Remember remote desktops address and logins.
3. Ability to transmit sound and video.
4. Transfer files to iOS.
5. SSH tunneling. I really hope iOS can support SSH tunneling at the OS level. Failing that, app level would be nice. BTW, where are the browser apps and twitter apps that support SSH tunneling. Hello, anyone? Alternatively, is there a write up of setting up VPN at home (with Mac) to substitute for SSH tunneling?