Inward Nozzle

Set-Through

• Advantages
• Allowed reinforcement credit for the full thickness of the internal portion (minus corrosion allowance) because this area does not need to withstand pressure. Can often do away with re-pad because of this.
• Makes for a great termination detail on linings, particularly brick.
• In abrasive service provides a nice "wear" corner so that you don't erode away the inside corner weld
• Where ancillary parts are required, such as vortex breakers, screens, etc, provides a nice convenient structure to weld to
• Can provide a gasket surface for an internal, reverse manway cover/door
  
• On a bottom section of shell can provide a "stop" for any foreign objects from entering the nozzle
  
• Easier to fit (doesn't require trimming) - especially on a double curvature wall (sphere, head, etc..)
• Eliminates the risk of lamellar tearing of the shell wall
• Disadvantages
• Can interfere with good flow characteristics/extra pressure drop
• Need access to the inside to complete weld
• If full penetration weld is required - adds to welding time/cost (depends on details) - may add post-weld heat treatment requirement
• Build-up against the wall of nozzle (silt, sludge, etc.) can create an under deposit corrosion issue
  
• Probably not even worth mentioning, but can be a little more painful to set right as the nozzle can fall through the hole

Set-in/on

• Pretty well the exact opposite as above

NOTE: that the second picture isn't necessarily a flat vessel, rather a longitudinal cross-section of a cylinder - in which case the fitting for set-on/in needs to only be done for a single curvature, and not a double plane like a sphere or head.