The choice between a bottomless (naked) portafilter and a spouted portafilter is partly aesthetic, partly practical. Both produce good espresso. They differ in what they show you and how the espresso lands in your cup.
Bottomless portafilter
A bottomless portafilter has no spouts and no bottom plate. The basket is exposed underneath, and you can see the espresso emerging directly from the bottom of the puck during the brew.
Pros: visual diagnostic of every shot. You can immediately see channeling, where one part of the puck gushes water before the rest. You can see whether your distribution and tamp are even. The espresso also does not contact spouts on its way down, which some drinkers feel produces a slightly cleaner mouthfeel.
Cons: splashes more, especially at the start of the shot when the espresso first emerges. You need a clean cup directly underneath, no gap. Cannot brew two shots into separate cups simultaneously.
Spouted portafilter
A spouted portafilter has a metal bottom with one or two spouts directing the espresso into your cup or cups.
Pros: clean delivery into the cup. Two-spout versions can split a double shot into two single-shot cups, which is useful when serving multiple drinks. Less mess. The portafilter also stays cleaner externally.
Cons: hides what is happening at the puck. You cannot see channeling until you taste a bad shot. The metal contact may slightly alter mouthfeel, though the difference is small.
Which to use
For learning espresso and dialing in new beans: bottomless. The visual feedback is invaluable. You can see exactly where your prep is failing.
For routine pulls and serving multiple drinks: spouted. Faster, cleaner, more practical.
Many home setups own both. The standard one (often spouted) for daily use, the bottomless for occasional check-ins on technique. They are inexpensive enough ($30-60 each) that owning both is reasonable.
Naked portafilter handles for the same body
Most modern espresso machines use a 58mm portafilter, and aftermarket bottomless and spouted heads are available for the same handle. You can swap heads without buying duplicate handles, which saves money.