TL;DR - I write too much shit.
There are two different kinds of pumps being show - vaccum pumps, which pull air to suck the oil though the filter, and peristaltic (pressure) pumps that push the oil directly through the filter.
Vacuum filtration is usually cheaper and easier for people that do low volume filtration. The 500ml filters are usually under $20/ea, and good for like 50 vials or so (realistically, unless you filter in several stages, you'r probably going to get super sloooooooooooooow flow after the first 250ml or so). Getting something with a replaceable membrane makes it even cheaper. The vacuum pump is maybe $200, and you can use the same pump for other things, like, say, charging the refrigerant in your car. The biggest hurdle is finding vacuum line, since most air lines are intended for pressure and not vacuum, and will collapse under a hard vacuum. Practically speaking, you're looking at 30-60 minutes to do 500ml of oil if you aren't filtering it in several stages.
Peristaltic (pressure-driven) pumps and filtreation are fast. You can push a few liters through a capsule filter in under an hour. (They can also be messy as shit, and cost you 250ml of finished test if you don't use clamps to hold your PTFE hose onto the barb fittings of your filter.) Capsule filters are more expensive than filter membranes, or even disposable bottle top filters, and peristaltic pumps that will put out enough pressure to do anything can also be quite pricey. You'll need to get the appropriate size of PTFE tubing to run through the pump, since different pumps will use different size of tube, and figuring out which tubing you need can be a pain in the ass.. But did I mention how fast they were? If you're doing serious volume, then that's 100% the way to go.
In my opinion, most people that are home brewing are best off with vacuum filtration. Even if you're also brewing for your buddies, you'll be able to do sufficient volume without a problem.