HNC in Electrical and Electronic Engineering

I could do this or I could do the HNC in Engineering (General)

The difference is some of the units are different, but you can also choose some your units. For example you could do Robotics/PLCs or Quality and Process Improvement. Do employers look at the units you have done or even care which units you have done or just do they care about if you have an HNC or not?

At this level it won't matter that much which units you pick, but I think if the job/career that you're after has something to do with electrical engineering it would be more beneficial to do electrical/electronic engineering rather than general engineering.
That would also make more sense if you wanted to do a BEng in Elec Eng after you've completed your HNC.

As always, the answer is - it depends. If you don't know what engineering domain you prefer yet and/or you don't have plans on what path to take either in engineering career or with further studies at Uni, then I'd suggest general engineering as it will give you a wider exposure to the different applications of engineering. If you go that route, then I'd suggest selecting technical subjects as opposed to the generic ones like quality, production engineering or even management (some engineering courses have that option for some reason, fyi having done a management unit doesn't qualify you as a manager).
Reason for taking a more technical path is (for example) you can become a quality engineer with mech or elec engineering degree, but it's hard to become an elec engineer without prior technical training.

If you goal is getting a BEng then why not go straight to Uni? if you don't have the necessary A levels for that then you can do a foundation year at the Uni of your choice which will grant you direct access to the BEng course of your choice (assuming you pass the foundation year exams of course).