Just make sure it's not a quartz watch
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I think we can take 'wear' as meaning 'take it along'... although personally I would wear it, if you do have a failure you don't have to fiddle around/thumb the dive, plus you can make sure you keep both of them out of deco - and lastly it's interesting to see/know what the differences (if any) are in depth reading, NDL, nitrogen loading & other data
Might be worth mentioning here that if you use EAN you should set both computers, if you choose to use two, to the correct mix or your backup isn't going to track your nitrogen loading correctly
Agree about your second point, since there are other advantages to using the same brand and/or model - same battery kit, screen protector, strap/mount etc not to mention not having to remember two sets of operating instructions, display layouts, warning sounds/symbols and so on