Well clearly you don't need one of these!
Of the two you picked I would actually go with Toro. There is nothing wrong at all with the Briggs engine.
I have a mower with Honda engine that was given to me. It is a good starter, but service is irritating. There is no oil drain plug for instance, so I have to use a vacuum pump. Honda also has a reputation for valve trouble, and I have seen that. It will pay to keep the oil very clean.
Round here were we have vigorous grass growth, the lawn condo contractors use Toro equipment pretty much exclusively.
The other issue is that the Honda engine is quite heavy.
I'm not allowed to push mowers up slopes any more, so the nice young man who helps me does the hand mowing. He prefers the mower that has the Briggs engine, that I bought for $50 11 years ago.
That is the next issue. Do you need a self propelled mower? I don't know your lawn, but if it is a confined area with a lot to mow around, a self propelled mower is not an advantage. You might be better off with a smaller lighter mower, especially a mulching type rather than bag.
You can also usually find good used lawn mowers for pocket change if you look around.