Is there any difference in setting the Compatible Parameter to 126.96.36.199 vs 188.8.131.52 ? Are there any advantages / dis-advantages ?
The parameter is described in the Upgrade Guide. You cannot downgrade a database to a version that is below the version of the COMPATIBLE parameter. The COMPATIBLE parameter controls how data is written to disk. But it does not control the usage of optimizer features. There are a lot of parameter to control the oprimizer features. The OPTIMIZER_FEATURES_ENABLED is a parameter that you have to set appropriately to enable the optimizer features of the Oracle version. Tom Kytes discusses the difference of these two parameter in this article.
Check the below from Oracle 11G R2 Compatibility document:
Databases from different releases of Oracle Database software are compatible if they support the same features and those features perform the same way. When you upgrade to a new release of Oracle Database, certain new features might make your database incompatible with your earlier release.
Your upgraded database becomes incompatible with your earlier release under the following conditions:
A new feature stores any data on disk (including data dictionary changes) that cannot be processed with your earlier release.
An existing feature behaves differently in the new environment as compared to the old environment.
The Compatible parameter change is not critical if you are not hitting any bugs related with an earlier version, but is sometimes required to unlock new features released as part of the new release.
Generally only the first 3 digits are taken into account for the compatible parameter, so either one is fine.