I have been wrestling with these ideas for weeks. Here is where I netted out.
1. You will likely come out ahead if you invest the money, but depending on how long, it may not be a ton. I ran some calculations and on a 7 year time horizon, I would come out ahead by something like $10-20k. If its much longer, then the delta widens, so you need to figure out your time horizon, because that matters.
2. Investing, at least up front, makes a lot of sense on a fixed rate/payment mortgage from a risk mitigation perspective. The idea is that you are basically building a war chest to insulate yourself against catastrophe - meaning the cash is fairly liquid and you could tap into if you needed it whereas if you paid it in to your mortgage already you wouldn't be able to tap it - unless you had a heloc, but I wouldn't want to borrow if a catastrophe struck. You could also do this with cash, but for me I have an emergency fund, so I am investing it. My plan is to get at least a year's worth of payments invested, 1 so I have it and 2. so it is big enough that it will start to grow decently on its own.
3. Once that is done, because I am on a shorter time horizon, I will likely drop everything on the mortgage, or a heavier on the mortgage, some back into investments split.
People are pretty entrenched in their positions on this debate and some see this as completely black and white. I saw good arguments on both sides. At the end of the day, I didn't like the risk of carrying a mortgage long, but I also wanted to be on enough stable ground that by accelerating my principal reductions I wasn't leaving myself open to a ton of risk.
The good news is that whatever direction you choose, you are going to be ahead of 99% of everyone else - save for the folks on this forum that is.