The short answer is the .357 is likely the better home defense round for its pure stopping power compared with the .38 +p (let the arguments begin).
But there are many variables to consider, hence the longer answer.....
Both rounds will have a loud report and there will be flash when used at night, and yes, the .357 will be at a disadvantage here. But will it be enough to not consider it for use? I doubt it. You will be so jacked up on adrenaline in a firefight you won't notice.
Do you live in an apartment or mobile, where only a few layers of metal/stucco/chickenwire separate you from your family or the neighbors? You may want to consider regular .38 rounds as opposed to the more powerful +p or .357. There are rounds designed in all three calibers for this situation, but you are just as likely to have the box of whatever Wal-Mart had on sale around if this is what you take to the range.
As you are new to handgun defense (we all are, actually. I figure you mean new to handgun use or to tactical training), the thought of using .357 if you are not comfortable doing so will affect your performance with the weapon. Only practice, practice, practice will alleviate that concern.
I would recommend practicing with each round to determine what you are comfortable with, consider the sage advice that is due to follow in this thread, take comfort in knowing that each round is a proven stopper (arguments will ensue, but fact is fact: .38, .38 +p, and .357 have all made people equally dead), and the decision will likely shake out to be much easier than it appears now.