CDs, TIPS (Treasury Inflation Protected Securities), MBS (Mortgage Backed Securities), Munis, Corporates... these are all so called "debt instruments".
Your question is roughly equivalent to "What is the downsides to investing into Stocks instead of AAPL??" Well... sometimes AAPL goes up, sometimes it goes down. Stocks are... well... AAPL -IS- a stock.
Similarly, CDs are typically a specific kind of bond: the type you get from a bank. But banks also sell traditional bonds.
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The main benefits of CDs is that they're (usually, but not always) FDIC insured. So if the bank goes bankrupt, the US Government steps in and will give you your money back.
The main benefits of "bonds" (which are a very, very broad category consisting of literally thousands, maybe millions of different things)... is that typical bonds can be sold on the open market.
That means that if the interest rates go down, you can sell bonds at a higher price. (Look, I have a 5% bond, and all you suckers are stuck getting 0.5%. Feel like trading? I'll sell you my $10,000 5% bond to you for $11,000.)
Of course, if interest rates go up, then bonds lose value. (Shoot, I have a 0.1% bond and everyone else has 0.5% bonds. I don't want to be stuck with this anymore, feel like buying this $10,000 bond off of me for $8500?)
CDs are FDIC insured, bonds aren't. This doesn't make a big difference when we're talking government bonds, but you can lose your shirt on a regular corporate/muni bond. You'll always get CD money back (subject to 250k FDIC limit)
Bonds also are also an asset that fluctuates in price: A bond can be sold at a price different from it's face value. This means that if interest rates rise, you're going to not be able to sell the bond for the same price you've bought it for. This is because you need to make up for the lower interest rate. CDs are just basically a loan on cash. Bonds are an asset (not cash!) that pays interest.
FDIC insurance is backed by the US Government. US Saving Bonds are backed by… the US government. They can be redeemed at any time, subject to certain constraints. They are not tradable bonds — a TIPS bond would be the US government instrument that is tradable and inflation protected.
In that context, the argument is that this can be a good place to keep an emergency fund, provided one has enough emergency cash in other places to bridge the first year before the I Bond can be first redeemed. The withdrawal penalty between years 1-5 is 3 months of interest, so not terrible if being withdrawn in an emergency.
No one's getting rich off this instrument, but it could be a good low hanging fruit option for some.
It’s backed by the full faith and credit of the US government and interest isn’t taxed until redemption, so it’s probably the safest/simplest investment for a retail saver that’s out there.