I suggest that you check the Main Project Documentation but I can summarize a few differences:

T4 Templates do not have indentation control (it's a major headache to adjust indents, spacing, and linebreaks).

In CodegenCS indenting works like magic - you can embed anything a text block (even multiline blocks or complex callback actions) and indenting is just preserved/consistent.
CodegenCS TextWriter accepts virtually anything embedded in the interpolated string but yet it preserves the indentation of the outer blocks.
This means that subtemplates don't need to worry (or even know) about parent block indentation level.

T4 has terrible support for managing multiple files: basically there is a single output stream and it requires a lot of hacks to break down the output buffer into individual files. This also means that multiple output streams cannot live together (you can't write to a file until you're done with the previous one).

In CodegenCS it's first-class citizen.

Other templating engines don't support multiple files at all.

T4 is like Classic ASP in the sense that you're just writing to stdout while mixing control logic within the output.

CodegenCS takes the opposite approach: we start with the control code (since it's just a C# method) and you have to programmatically write to the outputs. This provides more control.
The main magic is that CodegenCS TextWriter will take interpolated strings and the interpolated objects can be virtually anything: it can be another template, a callback action, an IEnumerable, inline IF/ELSE/ENDIF, IIF, etc.

Even though the library is primarily focused on "manually writing interpolated strings" it's still possible to have logic and output (you don't have "mixed indentation" like you would have in T4).
It also makes it much easier to output code without worrying about escape characters (think double mustaches or rendering ASP.NET <% %>).

The library is primarily focused in "manually writing interpolated strings" but yet it's still possible to have some control logic embedded in the strings:You don't need to do "foreach" just to render a simple list one per line.You don't need to write multiple strings to do a simple IF/ENDIF.etc.

CodegenCS templates can use Raw String Literals, which makes it much easier to write multiline blocks, indentation (combined with our implicit indent control), and makes it much easier to copy/paste between templates and output. It's also easier to identify what is control logic and what is output.

It's possible to use C#11 Raw String Literals even if the target project is not using C# 11 (output doesn't even have to be .NET)

CodegenCS templates can define their own arguments and options (using .NET System.CommandLine) and the CLI tools will show/accept/require those arguments.

T4 has poor intellisense and tooling.

CodegenCS templates are plain C# so they can benefit from amazing IDEs and intellisense.

CodegenCS has an out-of-the-box model that represents the schema of a relational database (with extractors for reverse engineering MSSQL and PostgreSQL), so it's "batteries included" toolkit (see quickstart)

CodegenCS is cross-platform. T4 is not. (is T4 currently cross-platform?)