I have a beautiful Model 66, and it's the most accurate revolver I own. But I also have 2 Model 10s from different decades and they're wonderful too. So why shoot .357?
Because I can.
My aim has gotten a lot better in the last two years. At one point I couldn't put .357 on the paper at 10 yards. Too much recoil, too much blast, I told myself. .38 is much more controllable. And it is. And .38 out of the 66 is great. But as I've practiced, and consistently hit with the 38 Spl, I've found the 357 Mag to be easier to handle. There isn't less recoil than 2 years ago, but I have a better grip, I'm using the sights correctly, and I don't flinch anymore. It was never about the round, but about me. I can shoot .38 all day long, and often do, but because .357 is a challenge to me I've become a better shooter.
All other things being equal, you'll pay less for 38 Spl, both guns and ammo. Don't pay attention to the writers in the glossy gun magazines who say that Thirty Eight Special is for retirees and housewives and won't stop a jittery cat. They all worship the 45 Ay Cee Pee, and spend $5000 to upgrade a 1911 so they can write about it. Again.
And the older .38s, from the 20s through the 60s, are little works of American art. Even S&W seems to have lost the secret of that wonderful blueing they used to use (the current blued Colts and Taurii are just mockeries of what was). People at the range with their plastic and stainless steel pistols will walk over to me and ask about them, and smile very broadly when I invite them to run six through the cylinder. A fifty year old S&W for $200 is within the realm of possibility, and still a great gun.
Either way is a good choice. Get the used S&W .38 Special now though--you can buy a new .357 later.