The 28J60 is much harder to understand and takes more experience to bring up. You don't seem to have that problem and since you can dedicate the entire arduino to sending a few bytes it is probably a really good choice. I have a few 'official' boards in operation as well as a couple of WiShields, they all fail from time to time.
You're exactly correct, it sucks to go hit the reset when this happens so I'm modifying my code to do a simple get to the gateway router to verify that the darn network is up for each device. So each device will do a 'get / \r\n' to the gateway router and if there is no response in a fixed amount of time the board resets itself. I've set up a laptop to watch the serial port for a couple of days and watched the devices recover from something and get back on line. Made the entire system much more reliable. You can go even further and reset the board at an opportune time (midnight maybe) to be sure something doesn't build up over time and even sample to be sure your sensors are alive.
So, I would go for the 28J60 for something like this and build in a series of checks to make sure everything is working, resetting when necessary. It won't hurt to put a web control in to reset the machine over the internet as well. This is actually kind of fun, send a command and the arduino resets itself. Not real useful, but fun.