I'll make it simple. The benefit for you would be the cost of transactions.

If you make a typical transaction with old type of wallet to old type of wallet, for 10 sat/vbyte you'll pay around 2570 satoshi. (see c71cfdbf267a23f1c512933d11305529f4dd9e036642ff11b4b26c38a25bd0ca)
If you make a typical transaction with segwit compatible wallet to segwit compatible wallet, for 10 sat/vbyte you'll pay 1660 satoshi. (see 0cdadafb139f58666a146d4627cb2e891db8d93d0ec5321a86d6f4a5cd07338c)
If you make a typical transaction with segwit bech32 wallet to bech32, for 10 sat/vbyte you'll pay 1410 satoshi. (see 116010d6a51087238ebc8f9e8e33a159ccee7f9fe818ef8aa00314bfd51f51e4)