Best third-party labs or engineers for specialized electrical product quality testing

I'd like to test the quality and performance of an electrical item I intend to sell.

I was able to find a similar, very high quality product whose quality I'd like analyzed and compared to lower quality alternative.

Who should I send these two product samples to? A  third party inspection company? a certain type of engineer? This product's industry is very specialized and the differences in quality may be subtle.

Don't know where you are based, but in NZ products are tested to a set of standards which are by and large international. In the USA Underwriters Labs have their own standards, the European standards have largely been adopted elsewhere in the Western world, Australia and NZ have some specific standards as well. It's actually a lot more complicated than that, but that sums it up.
https://en.wikipedia.org/wiki/Electrical_safety_testing covers the electrical basics.
So there are all of the basic electrical safety standards tests, then there are a whole lot of other standards based on the type of equipment being tested. For example, if plastics are used in the product, then specific test are needed to check parameters like flammability.
Specific product types also have a range of tests as well. Finger testing is designed to check that a standard finger can't come into contact through grills with live parts. The list is enormous, and for that reason you need to check with a engineer who does this kind of work. In fact, before you even design the product, it pays to check with them, since it is not unusual to have to face expensive redesign.
The tests must be done in an accredited testing laboratory(they have the appropriate testing rigs and test gear that has in itself been through an accredited calibration testing lab)), and it is not cheap.
If the product you want the comparison made against has been tested, then it should have the information on it, you can get copies of the standards and see what is involved yourself.
I have done testing work to numerous standards, interpreting and carrying out the tests is a long, involved process,
cheers,
Richard

Further to my comment, quality control is a separate issue from standards testing, and would normally be done in house by a person or persons trained in the area. It could covers all aspects of the process of manufacturing an item, from parts procurement (components and PCB) through to the assembly and packaging. In a large organisation, ISO 9000/1 acreditation would commonly cover aspects of this issue.
Performance may not necessarily require standards testing initially if all you require is a comparative analysis(which is likely to only cover electrical ), but if there is an electrical safety issue, then it definitely will eventually.
When you say that you have found a similar very high quality product, what are you basing that observation on, particularly as you say that differences may be subtle,
cheers,
Richard