I've been in the industry for some time and the only application where I've personally seen these t-body connectors used are in xfmrs, but I know they can be used in switchgear. Your picture showing the t-body connectors suggests very limited space for the terminations. A traditional bolted busbar application like your last pic requires a bit more "real-estate" to obtain proper busbar spacing, etc. This could be one reasons why they chose these style connectors.
I wouldn't necessarily say t-body connectors are better than traditional-bolted busbar connections utilizing standard crimp-compression lugs (the latter is my preference). The t-body connector can be purchased with a capacitive test point on the insulating plug which provides a means of testing the circuit without having to disturb the bolted connection. My understanding is that it provides hot-stick operable means of determining circuit condition. Also, if you have an application where a t-body load-break elbow is installed, a hot-stick can be utilized to connect (or disconnect) at voltage and under load. I've personally never come across this (nor would I have the guts to do it) but they're used in certain applications where power outages are extremely costly.
