Have a close look at what comparison you do with what object type. Have a look at this and how different comparisons work with different payload types:
[{"id":"bb4f191a.e43b68","type":"inject","z":"f954564f.03e718","name":"String 1","topic":"","payload":"1","payloadType":"str","repeat":"","crontab":"","once":false,"onceDelay":0.1,"x":190,"y":600,"wires":[["5606e10b.a83b8","9bdb6260.30e078"]]},{"id":"a2264de3.870e8","type":"inject","z":"f954564f.03e718","name":"String 0","topic":"","payload":"0","payloadType":"str","repeat":"","crontab":"","once":false,"onceDelay":0.1,"x":190,"y":660,"wires":[["5606e10b.a83b8","9bdb6260.30e078"]]},{"id":"5606e10b.a83b8","type":"ui_template","z":"f954564f.03e718","group":"5b810075.4590d","name":"","order":2,"width":0,"height":0,"format":"<div>\n <p ng-if=\"msg.payload === '1'\">\n String 1\n </p>\n <p ng-if=\"msg.payload === '0'\">\n String 0\n </p>\n <p ng-if=\"msg.payload === 1\">\n Number 1\n </p>\n <p ng-if=\"msg.payload === 0\">\n Number 0\n </p>\n <p ng-if=\"msg.payload == 1\">\n Doesnt matter 1\n </p>\n <p ng-if=\"msg.payload == 0\">\n Doesnt matter 0\n </p>\n</div>","storeOutMessages":true,"fwdInMessages":true,"templateScope":"local","x":380,"y":660,"wires":[[]]},{"id":"2ca0a9b3.9056e6","type":"inject","z":"f954564f.03e718","name":"Number 1","topic":"","payload":"1","payloadType":"num","repeat":"","crontab":"","once":false,"onceDelay":0.1,"x":200,"y":720,"wires":[["5606e10b.a83b8","9bdb6260.30e078"]]},{"id":"907cc9aa.cfc438","type":"inject","z":"f954564f.03e718","name":"Number 0","topic":"","payload":"0","payloadType":"num","repeat":"","crontab":"","once":false,"onceDelay":0.1,"x":200,"y":780,"wires":[["5606e10b.a83b8","9bdb6260.30e078"]]},{"id":"9bdb6260.30e078","type":"debug","z":"f954564f.03e718","name":"","active":true,"tosidebar":true,"console":false,"tostatus":false,"complete":"false","x":390,"y":720,"wires":[]},{"id":"5b810075.4590d","type":"ui_group","z":"","name":"Items","tab":"b83efc1a.370b88","order":1,"disp":true,"width":"6","collapse":false},{"id":"b83efc1a.370b88","type":"ui_tab","z":"","name":"Scheduler","icon":"call_split","order":2,"disabled":false,"hidden":false}]
<div>
<p ng-if="msg.payload === '1'">
String 1
</p>
<p ng-if="msg.payload === '0'">
String 0
</p>
<p ng-if="msg.payload === 1">
Number 1
</p>
<p ng-if="msg.payload === 0">
Number 0
</p>
<p ng-if="msg.payload == 1">
Doesnt matter 1
</p>
<p ng-if="msg.payload == 0">
Doesnt matter 0
</p>
</div>
Johannes