The stock mani leaves exhaust pulses hitting the turbo out of phase (as do virtually all O.E.M. turbo/manifold setups. Not an issue for component longevity.
Turbos also aren't as wholly receptive to 'tuned" header length (equal length or not) as NA and SC engines since the turbo impedes the strength and timing of the exhaust gas reversions. Resonance tuning still works with turbo engines but not typically as effectively.
Moreover there are design tradeoffs with a log vs tuned length exhaust that NA engines don't experience, and that's disregarding cost. The comprises of either design are headache inducing.
Log manifolds typically have a short distance between the head and the turbo. That's great for spool time and available energy as Exhaust Gas temps are quickly transferred to the turbine. Less heat is also lost because there's less distance for the manifold to radiate heat. The shorter length also means exhaust velocity at the turbine will pick up quickly when the gas is depressed, further aiding spool time, although keeping heat in the turbo is more important.
However log manifolds lose out on pressure wave tuning which would improve parts of the powerband vs. a log setup and also improve spooling.
Tuned length headers on the otherhand can gain more power in partss of the powerband and improve spool time by controlling exhaust pulses. A tuned header coupled to a twin scroll turbo really shines. The out of time pulses can be isolated all the way up to the turbine wheel for faster spool time and maximum energy at the turbine.
But they typically lose some or all of the gains in spool time over a log because the longer tube lengths leak more heat out of the exhaust and the greater volume takes longer to get up to velocity and reach the turbine. To give a clue as to how important keeping heat in the exhaust and thus the turbine I'll leave an example of what some all out, max power teams do to keep heat in.
One team made a tuned header out of thinwall SS (counterintuitively thin metals leaks less heat), they then welded large SS tube around each runner to act as an insulator, and then wrapped it all in heat wrap. Intense haha.
So to answer your question of which is better. Well it depends. A well made and calculated out and well executed "tuned header" can outperform a well designed log manifold in almost every regard...... At a price. If It's just a header slapped together with arbitrary lengths then It's going to be compromising some aspect of power or spool time...
Longevity and cost also favor manifolds.
In the end the turbo, other flow mods and tuning will make a vastly greater impact in power than an adequate log manifold and a good tubular header.