Which connectivity option should I use? - response (1) by NetFx

I assume you are asking about the "Microsoft .NET Data Provider for ODBC" and the ".NET Data Provider for Teradata".
The answer is very simple; use the ".NET Data Provider for Teradata"; the top four reasons are:
1- Teradata supports the .NET Data Provider for Teradata. We do not support "Microsoft .NET Data Provider for ODBC".
2- ".NET Data Provider for Teradata" has custom features (e.g. TdDecimal, TdNumber and list goes on). 
3- Simple setup and deployment options.
4- ".NET Data Provider for Teradata" is faster than the "Microsoft .NET Data Provider for ODBC".