Hello Ana,
A bunch of things can affect the Shannon index. Switching from OTUs to ASVs can change it. 
The Shannon index uses a log scale, but it can use log2 or log10 or natural log, and all of these are perfectly valid nobody EVER reports which one they are using!
This sounds crazy. And it is. And yet if you look in the original Shannon entropy paper that has 69,200 citations, all three of these log bases are mentioned on page one:
The choice of a logarithmic base corresponds to the choice of a unit for measuring information. If the base 2 is used the resulting units may be called binary digits, or more briefly bits...
If the base 10 is used the units may be called decimal digits...
In analytical work where integration and differentiation are involved the base e is sometimes useful.
The Shannon index is totally arbitrary, but the difference in Shannon index between groups matters. I think you can safely report that the Shannon diversity is not significantly different between these two oral microbiome samples.
Colin
EDIT
log 2(128) = 7
log 10(10,000,000) = 7
log e(1097) ~= 7
log (
) = 7