It will depend on a)the trail and b) the specific bikes compared. I went from a carbon hardtail (Kona King Kahuna) to a full suspension (Yeti ASRc) this summer. No noticeable difference on climbs, faster on most downhill segments (Strava!!!!!) Both bikes had similar drivetrain (2x10, but the Kona has a 39/26 crank and the Yeti a 38/24) and I used the same wheels on both bikes. The Yeti is about a pound or a pound and a half heavier than the Kona. Geometry wise, the Yeti is more aggressive than the Kona.

A full suspension bike will not only keep you in control, but also have better traction. This makes a huge difference on technical/loose surface climbs. And a decent modern full suspension bike won't lose much pedal efficiency. Probably balances out with the energy you lose on a hardtail due to bouncing over things and tire slipping.

In general, on smoother trails a hardtail will be faster. On more buff trails a full suspension will tend to be faster. Of course this assumes similar bikes. A 22lb full suspension bike will probably be more efficient than a 35lb hardtail even on fire roads.

If you have plateau on performance you need to identify if it is because you are at peak fitness or if equipment is holding you. Al lighter bike (or wheels, or rear suspension) may shave a couple seconds here and there. But unless you are making a huge change or addressing an specific issue (lack of confidence on descents for example) it is unlikely to make a huge difference.