The biggest disadvantage to you is that your tenant now knows your bank information, which means he can easily identify your source of money in the event he wins a lawsuit and wins a judgement. He will be able to have a court marshall freeze your account.
However, if you deposit your tenant's check into your account as opposed to an EFT, then your tenant can basically still obtain your bank account information and freeze your account, it would just take him a bit longer to get that information.
I am definitely anti-landlord in these situations because I've had to deal with so many bad ones here in NYC, but as a landlord, the best thing you can do is to create a "buffer" account for you to deposit tenant rent money into, then transfer the money from the buffer account to your regular account. This would prevent the tenant from knowing your personal bank information and greatly delay the tenant receiving his judgement from an assumed court win against you.
My source: I had to take my landlord to court, and after obtaining a judgement, I got a court marshall to begin the process of forcefully removing money fromclosing access to her account to me(she couldn't access the money in that account). The process resulted in her sending me a check (assuming from her other account) for the judgement since her account was frozen and she couldn't access any of her money.