The answer first.
Comparison pages usually bury the answer under a thousand words. These put it in the first line, name the one thing the choice turns on, and use the rest of the page to say when that answer flips.
AV Receiver vs Amplifier for Home Theater or Stereo
Buy the AV receiver if a television, a games console or a streaming box is in the system, because an amplifier has no HDMI input and cannot decode a surround track at all. Buy the integrated amplifier if the sources are two speakers, a turntable and music, where the receiver's entire video half is a fan and a menu you will never open.
HDMI ARC vs Optical: What Each One Can Actually Carry
Use HDMI ARC if the television has the port, because it carries the same Dolby Digital surround an optical cable does and it does it on the cable already running your picture. Reach for optical only when there is no ARC port at all. Neither one carries Dolby Atmos or a lossless track, and eARC is the only one of the three that does.
Home Battery Backup vs Generator for a Real Outage
Buy the battery if your outages run hours and you cannot safely run an engine where you live. Buy a generator if they run days, because a battery's capacity is fixed the day you buy it and a generator's is however much fuel you can get hold of.
Rope vs straight bar vs D-handle on a cable machine
Buy the D-handles first. A rope and a straight bar each do one job the other cannot, but a pair of handles is the only attachment that changes what you can train rather than how it feels.