How you evaluate risk affects whether you would rather have a paid for home or investments. To help you decide, answer this question for yourself, "If your house was paid for, would you take out a mortgage and put the money in the 'investment'?".
Probably. It depends on the investment vehicle, my goals, stage of life, etc. If I could be reasonably certain that the return on the investment would exceed the cost of the mortgage (which is tax deductible), I would not hesitate to do so.