If oldData keeps several objects, you can do:
if(!oldData.includes(newData))
EDIT 1 (for original code in description): if both are just single objects, simple comparison will do:
if(oldData! = newData)
EDIT 2 (for edited code in description):
addNewType(rowdata) {
    const newData = JSON.stringify(rowdata.value);
    const oldData = JSON.stringify(this.items.value);
    if(oldData.includes(newData)){
        console.log('This element already exists in the detail list');
    }
    else this.addItem(this.createItem(null));           
}
EDIT 3: if oldData has newData at least twice
addNewType(rowdata) {
    const newData = JSON.stringify(rowdata.value);
    const oldData = JSON.stringify(this.items.value);
    if((oldData.split(newData).length - 1) >= 2){
        console.log('This element already exists in the detail list at least TWICE');
    }
    else this.addItem(this.createItem(null));           
}
or:
addNewType(rowdata) {
    const newData = JSON.stringify(rowdata.value);
    const oldData = JSON.stringify(this.items.value);
    let newReg= new RegExp(newData, "g");
    if((oldData.match(newReg) || []).length >= 2){
        console.log('This element already exists in the detail list at least TWICE');
    }
    else this.addItem(this.createItem(null));           
}