A bit vague, but
Example of a sphere tee, sometimes also called a flow tee
Example of barred tee.
Sphere tees, as their name suggests were used when spheres were more commonly used to separate products and in place of pigs. When traversing reasonable sized tee, if only bars were used, they would stop as flow would divert round via the tee, hence narrow slots were required. To avoid excessive pressure loss on the tee connection, these narrow slots extend all the way round the main header hence require the outsize sleeve.
Plus point for sphere tees - You can send spheres down the line and the bars won't fall off or corrode
Minus points - they cost more, they can accumulate water, dirt etc inside and are a corrosion trap.
Reverse these plus points and minus points for barred tees.
Some operating companies, especially those in existence for a long time, can prefer sphere tees as this is what they are used to, but since I left that operating company some 20 years ago I haven't seen one since either in real life or design. Come to think of it I haven't seen a sphere for along time either...
My motto: Learn something new every day
Also: There's usually a good reason why everyone does it that way