Neither;
until you be more specific about your application.
We're not in the Racer's Forum, so I assume you're not building a race car.
A 550+hp 340 cid Hot-Rod streeter, normally aspirated, is a bit of a beast. I wouldn't recommend it. I was involved with a 500hp 340 street E-body, and the guy who insisted on it being a 340cid, was more than a little miffed when all was said and done. Thankfully, it was not built to be a streeter, but a showcar.
For a city car, I see no good reason to install an od.
A 350/400hp NA 340 can be combo'ed without an overdrive.
On the low end, od would be optional. Closer to 450hp, and still cruising the hiway, well now, od could be preferred.
But honestly, it depends on a few things,like; mostly the size of the cam, how much hiway you drive, your stall and gears, and availability of a bigger engine or a stroker kit.
Maybe you just picked 550+hp out of a hat, IDK. Normally-aspirated, for a streeter, it's probably best to top out around 1.1 to 1.15, maybe 1.2 hp per cube. With a 340, yur looking at 375/400hp. If you really have to have a NA550+ hp with a 340, then you're looking at stroking it to a 416 which is IMO still borderline too small for a 550+ hp streeter.
And besides all that, what are your plans for solving the traction issues? I mean even 350/375hp is gonna smoke the street tires to somewhere North of 50/60 mph.
And then there's bracing the body; and
cooling the beast, and
Fueling the beast, and
firing the beast.
But to sorta answer your question;
I have had good success with my GVod behind my A833/367 cuber.
