Since you are trying to perform two different modifications here is what support would recommend:
1. First upgrade the database on the existing platform. This will give you less "new issues" since you will be on the same platform.
2. Complete the upgrade of the RDBMS ALL THE WAY until production and release it to end users. Let the upgrade db run on the existing platform for 30 days so you have the opportunity or running your month end processes etc and are comfortable with the upgrade.
3. If there are any issues related to performance, resolve them while staying on the existing platform.
4. Then migrate the db to the new platform Linux and test it thoroughly. Create dummy databases and run all your batch processing on that dummy several times so you have addressed each issue. There should be NO process that will run on the final upgraded version that you have not run on the dummy testing environment. That is the only surefire way of addressing such a migration.
Depending upon the number of critical business functions and integrations with internal and external systems, planing and simulations are key for the success this project. Please document everything and analyze.
Testing, validations and performance acceptance are the key factors. Nevertheless, one key factor is size of DB, external custimizations and duration of acceptable downtime for busiess during migration weekend.
As Ram indicated when preparing base platforms, you have to consider OS, DB and Application patches as a starting point along good hardware. . Best of luck.
I already did a move from HPUX to AIX, that's not straightforward. The database can probably be moved relatively easy (RMAN), the application has to be installed from scratch (it can be prepared on a test server with same nes OS, and copied). But here start the pain with COBOL, interface, SQR... without saying to decomission the old env. to avoid connection out there after the move...
Obviously, all has to match with hardware level requirement and DB/Appl certifications.
A very good project !