Joined today and asking this? We deal with a lot of electronics and such around here, and there are plenty of members in such fields. but there might be better places to ask. Where are you doing this? I can tell a fair bit from the subject headings you mention but there are some substantial differences between mainland China, Hong Kong, Japan, North America, Canada, Germany, the UK, somewhere in the rest of Europe, Australia... as well as places within each of those (compare a shady for-profit school in the US to one of their top ones and the difference will be staggering).
Web dev would allow you to skip into electronics? Curious. Most web devs I meet I would hesitate to allow to rewire a plug. I can see being a web dev already allowing you to skip part of a web dev course and maybe some types of general programming if you did well on an interview or test but not electronics. On the other hand we may have different definitions of web dev -- someone tells me they are a web dev and I will probably assume they are either a php-mysql dev, ASP/.net-mssql or maybe oracle, in some places I might add ruby on rails or python, or perl if they tell me they have a nice CGI script. I don't doubt someone with those skills could be given a copy of the arduino programming IDE and have it blinking LEDs in response to inputs, and doing maths/timing related things on each of those whilst understanding what they were doing far more quickly than someone that just came out of high school and only has done maths and physics but I would not expect them to truly appreciate the idea of pull up or pull down resistors, never mind something more complex.
"narrowed down"
You are not going to be able to turn around and become a dentist or something without retraining but if those are the sorts of subject headings you will have a fair few things open to you either way. Are those headings all the years of the courses or just the ones you would be going into?
If you did embedded you might have an easier time getting into traditional embedded electronics where you would not be called upon to design my new motor. On the flip side traditional embedded electronics is not dead but not healthy -- I end up designing... new electronic locks for a security system. I am going to need someone which knows programmable devices but I will probably take the guy that knows enough to start playing with linear actuators and such, and has some mechanical engineering skills, right away over the other which could also handle the embedded stuff (maybe better and faster but if the job gets done either way...). Or if you prefer have you ever had a charge port become loose in a laptop/phone/whatever? Bad mechanical design got you that -- no sane mechanical engineer would want to put a surface mount joint subject to the kind of abuses you see phones take which is actually a lever magnifying forces and only bond it to a layered PCB with solder. Ever had a motor fry something when spun around because someone did not put a flyback diode on there? Or if you prefer why you are told not to spin laptop fan motors with canned air. Usually someone steeped in digital electronics but hazy on the analogue world what did that, or someone being cheap and not understanding the implications of their decisions.
I hate what the term "the internet of things" has come to mean but there is something to it and it likely will be the bread and butter of electronics in the future. If you then come to think the sensors you are using are just data input, which is unfortunately quite common among embedded and general programmers, and don't understand the mechanics of things you could end up struggling, or missing something obvious. On the other hand I have to have some optimism and assume the digi elec course will cover some of this as they have seen it coming.
5 to 10 years ago there probably loads of work to design a nice little device with a touch screen to diagnose a whatever, nowadays you throw all the data over bluetooth to an android phone or tablet and have some java dev handle the lot. Or if you prefer
https://www.theregister.co.uk/2012/04/03/software_patent_disabled_children_ipad/
That was 2012 when a device costing $7000 USD was rendered pointless by an ipad.
Alternatively alternatively how many digi elect students are there being pumped out into the world? In my experience those with strong analogue skills are rarer, and that may lead to it being easier to get a job in that than someone looking at a pile of 100 new graduates, all of which will be able to program their microcontroller acceptably. I don't know the numbers right now, much less for all the countries I listed in the start, so I will have to leave that to you.
Back to differences between countries then depending upon where you go you can transfer courses, pick options in later years and bias things towards your interests, though in some places that is harder than in others (in the UK I had one choice in the second year, and 3 from a list of 5 in the third year and that only amounted to a quarter of the hours I did in the case of the third year, in the US system that is practically unheard of). Beyond that you can always learn something on your own time, and once you have got out into the world and are somewhat established then your degree starts to matter less and less in the face of what you can do.
