It's pretty much unanimous that sumps are the best way to go as far as filtration. But WHY? I keep hearing that sumps are better because it makes escape harder for the octopus, but in what way?
Say you're a salesman. Try to sell me a sump.
A sump provides three major impactive functions for any tank. First it adds water volume (there are aquarists who install sumps are larger than their display for this advantage). Second, it provides greater aeration, keeping the oxygen levels higher in the tank. Third, the overflow design removes water from a larger area than a canister tube, cleaning more of the water with each cycle. Optionally, a cooling fan can be added to provide heat removal through evaporation (roughly 4 degrees below ambient in my case) and heaters can be placed where no animals will contact it.
Additionally, a sump provides both esthetic and maintenance enhancements. All the cleaning equipment is kept in the sump (filtration, skimmer, etc). Since a sump (used as only a sump) does not require any lighting or top, accessing the equipment for cleaning and maintenance is much easier and more likely to be done on a regular basis. In the case of an aquarium where an escape lid is necessary (for octos, of course, but also for eels and other carpet surfing critters), the primary tank can be fully covered with only small holes required for power head wires. A sumpless tank will require a canister filter that not only has small water volume and limited intake but builds up detritus and requires a frequent major cleaning effort. Sumps can be set up with something as simple as a filter sock with a bag of charcoal placed beneath the inflowing water (my preference).
In addition to the primary advantages, there is additional flexibility for how an individual aquarist uses a sump. My personal choice is not to add complications but many people choose one or more of the following:
Additional biological filtration:
Bio Balls or pieces for rubble live rock can be place in the water flow.
A deep sand bed can help export nitrates, especiall in a long term setup. IMO DSB's are not for beginners and the desired effect takes more than a year before detectable. If this interests you, read on DSP's before planning one. They work in the long run but understanding how they work and planning the design is important.
A refugium. IMO a fuge should be separate from a sump. A refugium has several advantage for water quality as well as growing out small food critters but is most effective when placed above and over flows into the main tank if growing out small food animals is the goal. It requires lighting and takes away from some of the ease of use but many people do a mini-fuge by adding macro algae to help export nitrates. Setting up a fuge in a sump usually requires partitioning it and advanced planning.
Additional mechanical filtration:
Hardware for nitrate or phosphate removal or CO2 reactors (corals) is far easier to add to an open sump than trying to put something in the main tank. A main tank option is almost impossible if you start adding hardware.
the only other option that i kind of like, is getting an oversized tank for what you want to do, and building filtration into the tank, and separating it with a partition. i mean, if your really pressed for space, dont want a huge setup and want to tinker with a diy project, that would be an alternative that i would consider. but HOB filters are, at least in my mind, very unfortunate.
You're talking about a AIO tank (All-In-One). That's how I designed my 50 gallon bimac octopus tank. I would have used a sump, for all the reasons discussed, but I chill my tank down to 56 degrees F, and so I wanted to reduce the amount of surface area per gallon, so I could more easily keep the heat out. I also wanted to use the space inside the tank stand (ventilated) for my chiller. I think a sump is easiest and best for a warm system though.