As others have mentioned, airlines generally want Part 1 PIC time for candidates.

As a former Pt. 91 Chief Pilot, I would personally log both Part 1 and Part 61 TPIC, and use whichever a given airline application calls for...assuming your Part 61 TPIC is flown from the command (left) seat. Part 61 TPIC is useful for many bizav jobs (people that understand the crewing dynamic is somewhat different than the 121 world) as well as bizav insurance documents.