Both good guns. I own a couple P08 Lugers, and one lonely P38.
Surprised nobody belly-achin' about the P38 heel mounted mag release!
I've had to tinker on my first Luger....it was a 'Jam-O-matic' when I got it. The second one works great, and they both work fine now after I re-sprung the first one.
The P38 has worked fine from the git go. But I think it was made in the last days of WWII, and went into Russian captivity with hardly any use.
I would choose the P38 myself. Not so picky about the ammo power. Lugers need ammo of a certain power level....not really 'hot ammo', but feeble ammo won't work at all. The P38 seems less sensitive to weaker ammo.
As an example of the P08 having ammo issues...A few months back I bought a box of my Lugers favorite ammo Winchester white box 115gr stuff. My Mauser made Luger fell on it's face with the stuff....an older box of the same shit worked fine...the ammo had been 'Obamaized'...was weak I guess. I bought a few boxs of the same stuff a month back, and it works in this Luger too. The old DWM Luger would eat either bunch of ammo, but not lock back with thwe weak stuff...it wears a new Wolff mainspring.
The late war P38 seems to like anything 9mm(don't shoot +P in these relics).
The US military has flirted with both pea-shooters in the past, and couldn't quite bring themselves to adopt either one, although the Beretta M9 has ancestory in the Walther P38.