In HoD, and certainly in single player, Planned Economy > LF. You get an additional 5% throughput, and no pesky capitalists. The only problem is that you have to buy all your railways yourself, but that's not a really big deal.
LF gives +5% output, thats way better as it directly increases profit.
Anyway, the economic policy is purely a personal thing, some players like to micromanage the shit out their economy, others don't want to do anything with it.
I mostly go for no subsides and build some factories on state capitalism, as subsides screw your budget and you need factories to get rich capitalists.
Apart from the wierd output bonus, the only thing i like about LF is that i don't have to constantly disable subsides (couldnt paradox add an option to disable standard subsides?).
If you want to sit back and enjoy a war, go LF.
If you want to controll everything in order to boost your industry score, go planned economy.
If you want the power to act, but not the need, go state capitalism.
Interventionism is the worst IMO as it only allows subsides, which i hate.
As said before, it's purely a personal playstyle issue.