Is there any difference if I use my planet account to download planetscope images rather than using sentinel apps such as eobrowser or request builder. If i download an area with planet account, then download the same area with different time using eobrowser. Does it count twice the quota or just one?
It seems that data quality downloaded from planet account is better?
If you are using “Hectares under management” model, you can download the data for the same area from either of the APIs and you will only consume the number of hectares once.
There is no reason for data to be better - it is exactly the same data 
I would be interested if you elaborate your findings in more details.
I download with EOBrowser, the file extension is TIFF, while I use planet explorer the format is TIF.
The TIF file is fine to open with ENVI but the TIFF one could not be processed.
I do know know that if there is any difference
I see, so there seems to be some specific from ENVI, which I am not familiar with.
That said, GeoTiff exported from EO Browser is a perfectly normal GeoTiff and you cna work with it in various programs.