So I need a new lawn mower for my 1/4 acre lot. Looking at this one:
I noticed you can buy it with either a Honda or a Briggs and Stratton (for $10 cheaper) engine. Is one engine objectively better than other?
For $10? Go for the Honda. They have a reputation for making bombproof small engines.
But in reality, the B&S engines last forever with indifferent maintenance- when was the last time you heard of someone’s 4 cycle mower being unusable because of engine issues? Just about never is my answer to that- they just last a LONG time even if you don’t change the oil/filters like the manual says.
I am a bit weirded out by the “No Oil Change” stuff for the B&S engine though; that seems like a recipe to wear it out faster to me.
I’d go for the Honda. I’ve had a couple Honda mowers and the others I’ve owned had Briggs motors. Both ran good but the Hondas always seemed to start waaay easier. Like on the first pull even after sitting all winter. Briggs seemed to be more finicky to start.
Briggs & Stratton is crap in my experience. I used to be in the lawn maintenance business. Go to a dump or metal recycler and see what has ended up there. Honda is great.
I think both engines can develop starting problems but those tend to be due to using gas with ethanol and storing the engines with gas over winter. Use ethanol free gas and empty the tank and run the carb out of fuel before storing for winter and those starting problems will disappear. Both engines will last a long time. That said, I would probably get the Honda 
I had a Honda mower, I think it was a 214, for over 30 years. The engine almost always started on the first pull as long as I had it. The mower deck itself was where it failed. I gave the mower to a guy who put the engine into a go kart for his kids. as far as I know it is still running.
Last summer I bought the new version of that Honda mower
TMMV
Toro mower owner with Brig’s and Stratton engine, I actually own 2 of them with that engine.
The first one started mostly on the 1st pull most every time, occasionally on the second pull for 15+ years and counting. For the first start of the season I’d say it was a 50-50 split between 1 or 2 pulls. This amazed me as I always expect some struggle but it never happened. I think I changed the oil 3 times in that time. Also even though the mower did hit some rocks and roots it is still in balance. In short it’s been a tank, throwing everything I can at it and it still runs like a top, including the personal pace self propelled function.
The second one I bought used for my vacation house. It also runs good, starts on one or 2 pulls but seems a bit rougher than my own one. I think that is due to ethanol containing gas (which I don’t use un my personal small motors, but other people do). I suspect a $15 carb replacement would smooth that out but it’s not that bad to worry about.
So all in all the Brig’s and Stratton seem to be solid engines, however I have heard great things about Honda’s engines and for $10 I would be tempted to go Honda.
My thoughts as well.