Speediness of initial installation and network synchronization
After initial installation, SPV wallets and full wallets need to download blockchain data from other nodes on the Bitcoin network. However, an SPV wallet only has to download block headers and some data specific to Bitcoin addresses it's responsible for maintaining. Hence, an SPV wallet can synchronize and be ready for use in less than an hour, whereas full wallets might take many hours to initialize.
Speed of new payments
For SPV wallets and full wallets, new (but still unconfirmed) transactions made on the network are quickly broadcast to all peers. If someone sends money to an address managed by your wallet, you'll be notified within a few seconds, no matter your wallet type.
Security for new payments
A full wallet that can access a complete blockchain can quickly validate new transactions, ensuring that it is sending money from a valid and adequately funded source address. An SPV wallet cannot do this and instead relies on its network peers to ensure its transactions are legit. In theory, if someone sends you a payment and is in cahoots with one of the (supposedly) random peers your SPV wallet interacts with, this sender could send you fraudulent payments. A full wallet is immune from this type of attack.
Security of confirmed payments
Even if a transaction is 100 percent valid, just because a transaction is broadcast doesn't mean it will make it into the blockchain, especially if the spender creates an additional transaction that attempts to doublespend the money to another address. For this reason, it's best to wait for three to six block confirmations on larger purchases. SPV and full wallets can validate transactions by tracking these confirmations. While a full wallet can directly prove that a transaction that has been mined into a new block is truly valid (i.e., sent from a fully funded address), an SPV wallet cannot. Therefore, if a miner includes a bad transaction in a new block, an SPV wallet could still be fooled. But it is very unlikely a miner would ever do this: Mining blocks is extremely costly, and by design a block with bad transactions would be immediately abandoned by any other full nodes on the network that take the time to perform validation on the block. As a result, a miner would never receive a reward for mining a block containing bad transactions. Hence, a confirmed payment sent to an SPV wallet is quite secure, although the security of a full wallet is still the gold standard.
All in all, a properly programmed SPV Bitcoin wallet can offer security for your bitcoins and bitcoin payments that is quite good, though it can never match the security guarantees of a full wallet. If you're running an SPV wallet on your smartphone and receive a payment, you can rest assured that once this payment has been confirmed by a few blocks, the balance and other information reported in the SPV wallet can be trusted to be accurate.
Efficiency of storage use
As discussed earlier, storing the blockchain of a full wallet consumes many gigabytes of disk space. However, an SPV wallet requires less than a gigabyte of storage and can run efficiently on a modern smartphone.
Ability to inspect arbitrary Bitcoin addresses
Because a full blockchain contains the balances of all Bitcoin addresses in existence, a full wallet lets you easily check balances and other details of any address, even those you don't own (if the full wallet programmers choose to include this ability in their app). An SPV wallet is completely ignorant of all Bitcoin addresses other than those it is directly responsible for and is unable to provide such information.
Ability to import private keys
If you want to import an existing Bitcoin address (and associated private key) into a full wallet, the full wallet is able to incorporate the address and the funds linked to it within seconds. An SPV wallet has no easy way to import such a key, because it has no information about any
historical transactions involving this address. Therefore, if you import a private key into an SPV wallet (given there is an option to do this), you can expect to wait several minutes as the wallet queries its peers for historical data involving the new address.
Effect on overall health of Bitcoin network
For the Bitcoin network to remain healthy, all the participating nodes need to cooperate in validating new transactions and blocks. As discussed previously, SPV wallets are limited in terms of validation capability. Also, SPV wallets usually don't accept incoming TCP connections and may not participate in broadcasting third-party transactions/blocks to peers. For this reason, having a large percentage of SPV nodes on the Bitcoin network could potentially have repercussions on the overall health of the network. At this time, there is little evidence of any negative effects. But as the blockchain grows year after year, the percentage of nodes that can't perform full validation may increase, and problems may arise. Nonetheless, improving storage capacity and faster network speeds will likely continue to allow people to cope with the growing blockchain, and definite benefits will be gained by running a full node. Hopefully, this will give many people incentives to run full nodes in the years to come to sustain the health of the network indefinitely.
In short, SPV wallets have some limitations, but as long as you understand these limitations, these wallets are suitable for storing your money. However, if you are storing large amounts of Bitcoin, it may be wiser to use a full wallet, given the additional security guarantees. But for storing some spending cash on your smartphone, SPV wallets are an ideal solution.