The White House message during the shutdown has been that there is a "national security emergency" at the border -- Sarah Sanders used these exact words this morning -- and the Situation Room lends an air of seriousness to the debate for the White House.
The Situation Room is also typically a no-press zone because it is a setting for classified intelligence, which means there is no opportunity for cameras or questions (although rare exceptions have been made in the past).
Having no press in the room means private discussions can be had, and it effectively blocks another photo-op moment between Trump and Pelosi and Senate Minority Leader Chuck Schumer from happening.
The invitations also didn't use the word "briefing" this time, -- it's just a meeting between principals. As a result, many on the Hill are expecting it will be just talks, but Democrats are also expecting the White House to put on some sort of show -- similar to the Homeland Security Secretary Kirstjen Nielsen briefing on Wednesday -- which was not classified and could have been held anywhere in the White House.
The bottom line: Trump likes the gravitas and air of seriousness the Situation Room brings even though it is technically just another conference room when national security and classified information is not being discussed. The Oval Office, which is traditionally used for meetings with Congressional leadership, would serve the same purpose in theory.