I have two repirts - One consists of campaign name further breakdown is done on marketing channel basis.
Other consists of campaign name and further breakdown is done on the basis of campaign medium.
Whats the difference between the two and which one qualifies to measure for traffic campaign traffic for a particular channel?
I assume that both "Campaign name" and "Campaign medium" are derived from your Tracking Code variable, which means those two are classifications of Tracking Code. In that case, Campaign name and Campaign medium would also have the same Expiration as your Tracking Code variable (which defaults to "Week"). Keep that in mind.
On the other hand, Marketing Channels are set with every hit. So it is possible that while your Campaign name and Campaign medium still persist during a week, the visitor could have another Marketing Channel set with some of his visits (e.g. if he came via a Referral). In that case, breaking down Campaign name by Marketing Channel (and/or Marketing Channel Detail) may not yield the results that you're expecting (although the results are correct if you're able to think through the expirations properly).
To keep your report easy to understand, I suggest using your second report, i.e. Campaign name by Campaign medium.
For the first report: One consists of campaign name further breakdown is done on a marketing channel basis.
While the second report: Other consists of the campaign name and further breakdown is done on the basis of campaign medium.
These two are different reports. The first is to populate channels based on marketing channel processing rules set up for the report suite.
You can read more about marketing channels processing rules here https://experienceleague.adobe.com/docs/analytics/components/marketing-channels/c-rules.html?lang=en
The processing rules might have been set up using campaign and campaign medium at your end to identify channels