I don't say there's NO difference.
In fact, in some cases, the differences are medium-sized.
However, in the critical-to-saving-the-nation issues, the differences are either tiny or non-existent.
Your example of the EPA is a good one.
The Environmental Protection Acts of 1971 were, and are, unconstitutional. The People of the United States delegated "all legislative powers herein granted" to a Congress, and We defined the process for making laws.
We did NOT authorize Congress to delegate any fraction of legislative power (we gave them ALL such powers) to any other entity.
The EPA was created by executive order of a Republican President, and the enabling legislation had overwhelming GOP support.
Ay Republican in Congress who does not favor repeal of all legislation pretending to confer any powers whatsoever on the EPA might as well be a Democrat.
technically, by stretching the interstate commerce clause, obama can regulate when you can go to the pottie or how much make up you wear or what color car you can drive