I visited a friend this weekend that had a Link and the controller and I personally think they're awesome. The thing is, the Steam controller is really hit or miss with your preferences.
Depending on the ages of your kids, I would say the controller learning curve can be a little steep. Especially if they're already used to more conventional controllers. Also, there's support for games but it's not exactly plug and play. You'll have to take time to set it up depending on the game.
As for the Link, it's pretty awesome but you'll need a router with 802.11 AC for the best performance. You can plug a wireless keyboard and mouse if you want. It supports most out of the box. It's a fairly straightforward streamer that works as long as you have the bandwidth.
TLDR: You have to try it out somehow. If you haven't, then it's hard to say if it's for you. These are not for everybody.