You should use the GATE score whichever is higher for admissions.
In Spot round anything can happen - and CCMT procedure itself is quite qumbersome. I suggest you to carefully see the CCMT cutoffs across different rounds. Spot cutoff won't be on CCMT- this you can know only from individual NITs.
Spot admission is also based just on GATE score- only the minimum % matters which is usually 60% for most NITs.