The difference is that transactions made from SegWit addresses cost less fees, so yes, it's better to use a SegWit wallet. And now the mempool is empty and fees are at their lowest so it is a great time to transfer your BTC to a SegWit address.

To answer this question, you have to know that there are two types of SegWit addresses.
 1)  P2SH SegWit nested addresses that start with '3' and as others mentioned not all addresses that start with '3' are SegWit nested but all SegWit nested addresses do start with '3'.
 2)  Bech32 native SegWit addresses that start with 'bc1'.
And of course there are the legacy non-SegWit addresses that start with '1'.

So what's the difference?
Bech32 native SegWit addresses are new and are not supported by all wallets and services yet. The result is that you may not be able to send your BTC to a native SegWit address unless you import your private keys into a wallet that support this type of addresses. While all wallets and services support sending to P2SH SegWit nested addresses.