When you are tenants in common (TIC) and one of you dies, the deceased owner's share passes in accordance with his or her will. When you are joint tenants, the survivor becomes the sole owner and the whole property will eventually pass under his or her will.
If you do wish the surviving spouse to own the whole property after the first death, you can apply to move the restriction or change your wills.
When you are joint tenants, in the eyes of the law you are one owner. This means that when you are means-tested (for benefits, say), each will be considered to own the whole of the property. If this does not worry you, consider the possibility of your spouse remarrying after your death and leaving the whole house to someone you would not approve of, or favouring one child in their will. The surviving co-owner decides what happens to the property.
When you hold as tenants in common, you only own your share and only you can decide what happens to it. When the first of the tenants in common dies, their heirs take their place on the register and become co-owners with the surviving original owner. When the second original owner dies, their heirs take the second share.
If both tenants in common die and the property is sold, the proceeds are divided according to their shares and distributed according to their respective wills. The buyer will take the property free from restriction.
To check the actual ownership of a property you can order a copy of the register from Land Registry for £3. If you'd like to have a chat about tenants in common, or other options for protecting the future ownership of your property, please get in touch.