ZigzagPX4
The Swiftness of the Ranger
I actually agree, Mr House isn't the best person but I think he would beat the Institute.
Only because he's well written and they're not.
Eh... that's not really fair. I suppose it's true we can't compare them as much as we would like to considering how vague Fallout 4 was with everything. But we can at least do a rough comparison.
And they were already making moves to take it from Mass Fusion, and nothing suggests the BoS would have beat them there had you not helped out. They were already on the way to fixing their biggest problem, and didn't even really need YOU to help them do it.
On the other hand, House is entirely without anything unless you help him because of consistent poor moves on his part.
Not to mention The Institute can make more super mutants to throw at House, on top of synths.
Well, unless we're going to consider the Institute an organisation with limitless resource and an endless arsenal, in which case they're just an overpowered, unbeatable Mary-Sueish version of Big MT, then we can't just assume the Institute could simply teleport ten squads of Gen 1 synths and six Coursers into the Lucky 38 and massacre the Securitrons there.
With sensible reasoning, the Institute's teleporter probably has limited range, not to mention a limited number it can send at a time. It's still a pretty large number, though. And there's nothing to say that the Institute can actually control the super mutants they create. Simply put, Mr House would not be able to mount an offensive on the Institute, but neither would the Institute be able to take him out. The Institute is at a point where no one can attack them unless they open up, but they're not gonna be able to take over the world unless they open up. That's why they have Kellogg, that's why they have you. A risk-free wildcard they can point at anything.