Right now a 406 small block motor (which is a lot more common than you might think because you can not go by the 327 valve cover decal) will put you on the trailer every time. You are running around with a motor that weighs 230 pounds more than his small block and your motor has smaller valves than his motor does. The only way a big block beats a small block is to make your displacement bigger than a small block (big enough to over come the weight advantage) and to install a better head (one that has bigger valves and modified ports to raise not only the air flow volume but the intake port velocity).
From the outside my 582 cubic inch big block looks just like your 396 (mine even has 402 decals on the air cleaner to help people identify what I am running; since you can not tell). Well actually I can tell, as can an experienced engine builder who knows what to look for; but I have been screwing big blocks together since 1965 when they first came out. Most people at a car show won't have a clue as to your engine size or if it is a Mark IV (396, 427, 454), or a Gen V (454), or Gen VI (454, 502, 572).
With the right block and heads you can make as much horsepower as you can afford. Heads are how the engine breaths and is your most important choice. The block is only important as there are three basic bore sizes offered with a big block (just think of the three bears). The middle bore size is your Goldilocks choice if your budget is limited (say you have kids to feed, or a mortgage payment to make every month). It is the 4-1/4 inch bore of the 427 and the 454. The larger papa bear 4-1/2 inch bore will make a boat load more power but they were never installed in a car, or a truck by the factory so they are the pricier choice.
So if you can find a 454 pick-up truck motor to supply the short block, and then buy a set of aftermarket heads to top off a fresh rebuild; you will be making 430 to 570 horsepower depending upon your cam and induction choices. Right now you are outputting 350 horse or so at the flywheel or about 280 horsepower at the rear wheels. Everything you have now will bolt back onto the replacement motor and as I said if you could hide the bills the wife wouldn't be any wiser as there is no visible difference. She might wonder why rear tires don't last very long though so don't tip your hand too soon.