Just because the Marlin is cheaper doesn't mean it's better.
You are right, cheaper doesn't always mean better. That said, in my experience (and I have owned a number of each) the marlin is the better gun between it and the 10/22. I have had a number of 10/22s and out of the box the marlin 60 is more accurate, and reliable with a much wider range of ammo, and it costs about 1/2. Now I have tricked out at couple of 10/22s and they were great ........ after I spent another $200 -$300 on them. I have owned and shot Mossbergs, stevens, remmington, browning, and winchesters, and for the money the little Marlin is the best value. It shoots as accurately as guns costing 3-4 times as much and they are in my experience more reliable with a wider variety of ammo than most of those same guns. BUT semi's of any type will rarely be as reliable as other actions. That is especially true of rimfires.
I have owned a number of different pumps and like the remington best. I have an old alloy rec. remington that is a sweet shooting thing. Very reliable, and extremely accurate.
In my experience bolt rifles are a little more price dependent. High dollar guns are usually that much better than cheapo's with the Anshutz being at the top of the ladder. But in the LT $300 range the Marlin is still a decent option. They shoot great, are tough, solid made, and you usually can find a decent used 25 with the synthetic stock for $100 -125. My only real complaint with them is the triggers which are ok, but not great.
As for lever guns, I have owned and shot Winchesters, Brownings, Marlins, the Ruger 96/22, and the new henry. Overall these are all great guns. IMHO the Winchester and the Browning are the "prettiest" of the lot, the Marlin 39 is the best shooter, and most solidly built (I own 3 currently), but unless you scrounge around all of these are gonna be above you $300 target. The Henry is a very good little rifle that is worth the money, but I would still hold out for the Marlin. They are built like a center fire rifle, tough, break down into 2 pcs for storage, carry, or cleaning, and unless they are abused they will be working well for the next 100+ years.
Now for the OPs question were I looking for a SHTF .22 it would be a little tube fed Marlin 25. Bolt actions have less that can go wrong with them than any of the other actions, tube feeding is more reliable (in my experience), plus the tube is less likely to be lost or damaged than a mag. For $300 you can likely buy 2 of them and a couple or three thousand rounds of ammo. They are accurate, reliable, tough made, and parts are readily available so you can stock some spare parts. Maybe that not as sexy as a tricked out camo tacticool 10/22, but I think it would serve a person well.