There are a lot of good answers here! I won't re-hash all of it, but I will say I have both high cash value life insurance polices and a self-directed 401k. I use both for investing and find myself looking for ways to put more money into the life insurance while looking for ways to get money out of my self-directed account. Why? Because I want to get as much of my capital into a tax free earnings bucket as I can and for me, that's real estate. I can buy real estate syndications and never pay taxes on the gains (Lazy 1031). With my self-directed account, I am partnering with the government because they will decide how much tax I pay and when I can take it out.
The question was - which should someone put money into - this is an unanswerable question because each person's situation is so different and these two products are, as others have said, comparing apples and oranges. They are both fruits, but very different.
High cash value life insurance is not an investment, but when used properly it can turbo charge your investments. The key is to have it set up correctly and for your specific situation. I used to sell these policies and the first policies I sold were to my wife and myself. I was trained to sell a specific type of insurance in a specific way - targeting high paid professionals who would use it for retirement. This is completely appropriate - except that wasn't how I was going to use it. I sold myself the wrong type of policy because I was inexperienced and I was following my training. I don't sell insurance anymore, but I still buy new policies and I have them structured by an agent I know, like and trust and someone who understands how to structure if for me to maximize cash so I can use it to turbo charge my investments. As an example, I use my cash value to buy ATM's. I take a loan against the cash value at 5.5% and put it into ATM machines which pay around 25% cash on cash. For round numbers, I take out $100,000 and pay interest of $5500 per year and earn $25,000 per year. After 4+ years, my loan and the principal is paid back and I collect ATM distributions for another 3+ years. At the end of seven years, the interest and principal is paid back and I have effectively manufactured $60,000+ in cash. For those four years that I had the insurance loan - the cash value was collateral, so the actual cash value in the policy continued to grow. I earned two returns with the same dollar and created cash out of nothing. I can't do that with a self-directed IRA.
The reason I still use the self-directed account is that I had some old 401ks that I rolled over - I use that money to invest in debt because if I invest in real estate through that account, I lose a lot of the tax advantages.
Again, it's different for each person - neither of these are bad products, they just have to be used correctly. Yes - Suzie Orman and Dave Ramsey say whole life insurance is a scam - but as was said above, they are financial entertainers. They have great advice for people deep into debt - they give terrible advice for people who are striving for financial freedom through investing. Both of them own whole life insurance - they just don't think their audiences are smart enough to own it correctly.
The key to investing is to have great partners - so if you decide to go with the self-directed IRA, whole life insurance or both - make sure that you have a partner who you know, like and trust that can give you expert advice. If you get your insurance agent from the yellow pages, be prepared to feel like whole life insurance is a scam. If you get your insurance agent from a trusted person who already uses that agent successfully, then be prepared to have a properly structured policy that can turbo charge your investments. I would say the same for any financial product.