I can't answer for cisco, but for Junipers I'd like the interface represented in a hierarchy like this (though rotated through 90 degrees)
[it was faster to use the visio org chart wizard to draw this]
Here I have an aggregated ethernet (ae) bundle with two xe interfaces and two VLANs on it.
I normally want to monitor:
a) the ae budle to see that it is not overloaded
b) each vlan in the bundle to get per-vlan statistics
c) the physical interfaces (so I get error counts at the interface level, and can tell if an interface goes down. FCS errors, runts, giants, etc. do not get rolled up to the ae0 stats.)
Junipers also create per-vlan interfaces below the physical interfaces, personally I'm not interested in monitoring those as they don't show anything interesting (that I can see).
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note: in non-lagged / etherchannel interfaces I would want to monitor the vlan interfaces below the physical interface because that's where the per-vlan stats are held.