The operating system and apps will all run about the same on both machines. The differences are in the hardware. The Samsung has a very small 16 GB solid state drive built in to the main board. It also uses an ARM CPU and GPU which is found mainly in cell phones and tablets. The Acer uses an Intel Celeron x86 CPU which allows you the option of installing Windows if desired. Also, it uses a SATA port for the hard drive. The Acer is ideal if you want to upgrade parts. It uses traditional RAM slots as opposed to the Samsung which has the RAM soldered to the main board just like the HDD. As for the screen, I personally had a Samsung version, the new $250 one. The screen is quite cheap compared to other laptops. It has a poor viewing angle and is hard to see in brightly lit rooms or sun light. I can't speak for the Acer, but based on reviews the Acer has about the same display, although it has a glossy screen as opposed to the matte finish of the Samsung. The choice comes down to personal preference. i prefer matte so you aren't seeing too many reflections.
In real life use, you won't notice a difference in CPU power between the Celeron and ARM. In benchmarks, though, the dual core Celeron is slightly faster than the dual core ARM most likely because it uses more watts to power it.
The Acer is much more versatile in terms of upgrading hardware and changing OS (if you want to) while the Samsung is more sleek, slightly more compact, uses less power due to the mobile CPU, which in turn means less heat and more battery life, and with the SSD it is slightly faster booting. An SSD also saves some battery life vs a mechanical HDD. You could always get a small 32 GB SSD for the Acer, upgrade the RAM to 4 or even 8 GB and it will match or even outperform the Samsung. Those upgrades would cost about $50 which would make it around the same price as the Samsung but with a bigger drive and more RAM. Personally, I'd get the Acer. I had the Samsung for a week and sold it on ebay. I did not like the operating system and the only other option was installing a limited functioning version of Ubuntu (no sound or camera). Everything on the Chrome OS runs through the browser. If you don't have an internet connection, the device is almost completely useless. One reviewer described it as "a glorified typewriter" when used offline.