1.First of all United`s service and on time schedule is poor. Their inflight entertainment and customer service is horrible if anything goes wrong. So if your flight is delayed or cancelled,they will be poor to deal with. No hotel accommodation, nothing -- things like that.
2.Connecting in Mumbai is a real hassle.You have to collect luggage and check in for the domestic connection. If your bags are lost or delayed in United,you cant fly to Hyd and United will be least helpful and will be a nightmare.
3.And if you want to change your return flight from Hyd,it is very easy on Emirates or Qatar. They have very helpful local offices and you can change on the phone itself. And if your flight is cancelled in Dubai,they will provide you with excellent accommodation and meals. Also inflight entertainment on Emirates and Qatar are the best in class.^
But the most crucial thing is that you are checked all the way to Hyd-- no collecting bags in Mumbai and checking in for domestic flights again.It is so convenient and the chances of losing luggage are very small. You check your bags in SFO and collect them in Hyd !! Compare Emirates and Qatar air rates. Sometimes one is better,other times the other one has better rates !! Hope this helps.
Personally, if flying to India--I would never fly United , Air India or Air France. If flying to Delhi , a good alternative would be American or Continental though as they have direct flights from NYC to Delhi. Not useful to you but just some info.