Hi Richard,
You should be fine with 16.0 Open Server application to connect to ASE 15.7. Open Server 16.x is certified with ASE 15.7.
The major thing I see with your old application using old dblibs is if you have DBVERSION set to using tds 4.2. You will want to make sure the application is using DBVERSION_100 in the application, which basically makes the application use tds 5.x which is the current standard. I have seen the old flavor of tds cause stacks in the newer ASEs.
Also note the compile line changed since the older 10.0.4.And the binary names for the libraries you need also changed. Also note when you compile on the newer Linux systems your switches that are added to the compile will have also changed.
You can always look at the samples for dblibs included in the SDK for SAP ASE to see sample compile lines and switches used.
You honestly should upgrade the application to ctlibs to handle speed performance and threading for the faster ASE.
I hope this helps with moving and migrating the application.
Dawn