Probably the biggest advantage you will see mentioned is heat transfer and depending on the pump, this can be significant. For instance, the Magdrives are known for running hot. Other considerations may be power consumption, maintenance, convenience, plumbing concerns, voltage transfer, aesthetics, safety etc...
Internal pumps have the advantage of not being able to flood your house if they fail (not to be underestimated as an advantage). If someone just asked me to set up a casual aquarium for their home, I would say go with an internal pump and be done with it.
Having said all of that, personally I will say that I like having my external pump out of the sump. I also how sturdy everything is when its hard-plumbed, my Reeflo pump moves a ton of water, is bolted to the floor and certainly isn't going to shift around. It has also been running continuously for nearly a decade (except for the one time I had to take it apart to pull out a fish shipping bag and plastic shrapnel that had clogged the rotary--the pump continued with no issues). Reeflo pumps are not pressure rated and may (or may-not) be ideal for running lots of auxiliary devices like reactors, sumps, other tanks, etc... If I wanted to instal a separate auxiliary line pump for running reactors for something like a fish room, I would go with an Iwaki or panworld pump and just make that a separate loop so changes made there do not impact the flow to the aquarium.
