Which one will give me better performance for the least amount of money for casual web browsing (via Chrome Browser)?
I'm worried that the i3 "U" version (basically a laptop CPU) CPU won't be powerful enough for 10-20 tabs open at a time. If I build my own, I want to go with Silverstone's VT02 (coming out in late February/early March), which is a mini-STX case. I will use the Pentium G4560 (the new Budget King!). I'm not sure which motherboard I will use. Any suggestions? The features I want are M.2 PCIe SSD (NVMe support), as well as SO-DIMM RAM.
I could always get a Chrome device (i.e. Chromebox or Chromebook); do I have any other choice?
In answer to your question, roughly speaking, you can always get about twice the amount of computing power building your own STX or ultra-compact ITX system than you get with a NUC at the same price. That's especially true with the build you're thinking of, equipped with the new, as-yet-unreleased Pentium G4560 with Hyperthreading. It's Intel's greatest gift to PC enthusiasts since the overclockable Pentium G3258 released three years ago. In fact, I think it's an even bigger deal, because Hyperthreading is practically required for modern dual-cores to function well.
The STX format is really an exciting development for PC users. It's almost as small as a NUC, which means there are very few situations where a NUC would work but an STX system won't. I assume you've already seen TBG's coverage of the new NUC, STX and the SilverStone VT02
from CES 2017, but if not, definitely check it out!
As for particular motherboards and RAM, you'll have to wait on that, as new 200-series motherboards supporting the G4560 have not yet been released. But here's some good news for you: TBG already has a VT02 review sample on order from SilverStone, and it will probably arrive around the same time the VT02 becomes available at retail. We'll be putting together a complete step-by-step build guide using the VT02 and G4560 as soon as both are available. A monthly buyer's guide will also be created featuring this duo, replacing the current Antec ISK110/Pentium G4400