Disclaimer: I have an HTC Thunderbolt, not a Nexus, but I do have a Slingbox, and have been using it for years now (I'm on my 2nd one). I currently have a Slingbox Solo model.
First of all, to simply answer the question about using the slingbox on your phone...I find it works very well. i have both the phone app and the tablet version for my Galaxy 10.1. No complaints; it connects every time and I've never had any real issues with it.
Now, the actual quality of the video and your overall slingbox experience will depend on a few factors (regardless of whether watching on phone or remote computer via Internet)...
1. Your in-house setup. Slingbox requires component video for HD feeds. As far as I know, HDMI is not supported, so if you currently use HDMI with your cable box (or satellite receiver, etc), you may run into some problems.*
2. You home Internet situation. Slingbox requires a dedicated WIRED ethernet connection. I have attempted to use wireless gaming adapters with the Slingbox with a moderate degree of success, but the bottom line is that you REALLY want to have a wired connection available to run to your slingbox if you really want to expect it to work as described.
3. Bandwidth. This is on both ends. In order to get the best quality for remote viewing, you obviously need to have sufficient upload bandwidth from your home ISP. If you have cable or FIOS, for example, you' should be OK, if you have DSL or slower, your video quality will probably suffer. On the flip side, if you're trying to watch slingbox on your phone, obviously a 4G or Wifi signal will give pretty good results, but watching over 3G can will yield a noticeably more blurry and or choppy when it comes to video quality.
Bottom line, if you have a decent high-speed Internet connection available at your house to use with the Slingbox in a location convenient to connect to a cable box (or other compatible device), you'll probably find it works very well. If you're expecting to use WIFI to connect your slingbox to your home network or if you're expecting crystal clear quality while watching on your phone over 3G, you'll be quite disappointed. I'd definitely recommend the product, but also advise on evaluating how and where in your home you'll be trying to set it up and whether your home Internet connection is good enough to support it before making the purchase.
*Some devices do allow concurrent HDMI and component output, others do not. If you require an HDMI connection to your TV with the device you're planning to use, I'd test having component video attached concurrently with another display, or plan on only using the component video output. The standard Slingbox setup has you run the component video out to your slingbox device, which then connects to the TV via component output.