From what I gather, Joseph's politics were more explicitly anti poor and anti working class than Thatcher's, and he was less likeable to boot. So his premiership would be very similar to Thatcher, but a bit more extreme.
That is assuming he can become PM in the first place. Even if he didn't make the eugenics speech, theres a decent chance he could be beaten to the leadership by Whitelaw or some other wet. And if he polls lower than Thatcher, then maybe Callagham decides to head to the polls early in 1978 and is narrowly returned as PM. If all of that doesnt happen and Joseph wins in 1979 or before, I'd still expect him to have a lower majority than Thatcher, which obviously limits his room for manoeuvre policy wise. It might also leave his government vulnerable to collapse if there is a mass Tory defection to the SDP, something that was considered IOTL but failed to materialise. I dont know how he would react to the Falklands, or if that would even happen in the first place. A lot could depend on that.