I'm assuming you are asking from the investor's perspective. I believe both buying your own turn-key properties and making an LP investment in a syndication can both be a great way to earn passive income. Here are my thoughts on the relative benefits of each:
Turn-Key - Some quick assumptions: You are buying a property with a tenant already in place, have a great property management company, and the property doesn't have any deferred maintenance:
1. You can change managers - When you buy into a syndication, you are are completely dependent on the sponsor. If you are not happy with their performance, there is often not much you can do. However, when buying a turn-key property, you have the ability to find a new property manager, if you're isn't performing. Of course, how difficult this is depends on your contract.
2. You have complete control - If you decide to change to STR or spend additional money to upgrade the property, that's your decision. Of course, you have to wait for a vacancy. With a syndication investment, your investment is controlled by the sponsor and their business plan.
3. You have greater liquidity - If you own the Turn-Key property alone, you get to decide when to sell or refinance to get access to your equity. With a syndication, you don't get any control over this timing. You may be able to sell your LP position, but there is often a discount associated with doing this.
Syndication:
1. This is truly passive income - You don't have to make any operating decisions like you will with a Turn-Key property.
2. Not credit dependent - In many cases, you are not providing any guarantee, so you don't have to qualify for a mortgage.
3. Professional operator - Although you may be stuck with the sponsor, you also gain the benefit of their expertise. When you are doing your due diligence on a syndication investment, you should vet the sponsor rigorously. Great sponsors will have a track record of solid returns over time.
4. More product options - You can invest a small amount of money and still access large multifamily or commercial properties. To make a similar Turn-Key investment would require much more capital.
You can achieve strong risk adjusted returns with either strategy, but from what I've seen your upside as a syndicate investor is limited. This is why many LP's eventually move to the other side of the deal. In my mind, the decision comes down to how much you want to be in control vs. how much you'll benefit from a professional sponsor.
Full disclosure - I've looked into investing in syndications many times, but have always decided to invest directly in property instead. I have helped sponsors of syndications locate properties, and many of them do a great job for their investors.