Teak oils are made from Linseed oil, Tung oil, mineral spirits and varnish in various combinations depending on manufacturer, designed to soak in and penetrate the wood. Many of the popular alternatives are basically just a home-made version of "Teak Oil."
Sealers stay on top of the wood providing a barrier, made from synthetic resins.
As mentioned, the oil will need to be applied more often, but if you do it before its too dirty and worn, you can just do a re-application pretty quick....likely needed more than once a year. The sealer will last longer, but will take a lot more effort to clean up for re-application.
Thats all just preference AS LONG AS the sealer doesn't end up being slippery.
I used a sealer by accident once. It was a little slippery, and once it started fading and needing re-application, I had to pressure wash and sand to get all of it removed so I could apply an oil. Not doing that again. The lastest application was just linseed oil and mineral spirits becouse I had some on hand, worked great. I have the startbrite kit and the cleaner and brightener steps do a great job, and the teak oil that comes with also does a great job. I go through the teak oil much faster than the cleaner and brightener since I don't have to go through the whole 3 steps as often, so I jus substituted the linseed/mineral spirits.