CIE IGCSE English Language may be easier, since it is International GCSE, a lot of international students are expected to take it even though the name is IGCSE First Language English (there is also Second Language English for CIE IGCSE).
However, my school is an international school and it only offers CIE IGCSEs, I cannot make a fair comparison with WJEC or any other secondary education examinations.
I do agree though, some subjects in CIE IGCSE are harder than normal GCSE (No idea about Welsh examinations though). For example, CIE IGCSE Sciences are relatively more detailed than GCSE Sciences. We had textbooks made for GCSE Sciences, but because they were not detailed enough, we had to buy new books specifically made for CIE IGCSE sciences.
From what I see, History is also harder with CIE. I have seen AQA/Edexcel History papers and CIE seems to be harder. I can't explain how, they do almost the same topic, but the questions are a bit nastier with CIE in my opinion.
I also heard rumours that maths is harder with CIE but the questions are less wordy. It makes sense that CIE is less wordy because again, it's international = a lot of second language English speakers would take it. I am not sure about difficulty but as far as I see the past papers (just now I checked), CIE Maths is harder than Edexcel GCSE maths (not THAT different but still a bit harder, I think).
The biggest difference is NOT the difficulty though. The biggest difference is that due to the fact that CIE is an international examination, they do not specifically pick up British topics. This can be seen in Humanity subjects in particular. If you take GCSE (or the Welsh one) Geography, you will need to know Geography of Britain along with World Geography. On the other hand, with CIE IGCSE, they pick major MEDCs/LEDCs, and when they need example, they just pick a random country like Japan for ageing population etc, and for map skill paper, they often take a Caribbean island. Same goes for History. I suppose you need to do History of Britain along with World History when you are doing GCSEs (or Welsh one, dunno again), but if you take CIE IGCSE History then you will do normal World History like Cold War, Hitler's Foreign Policy etc, and you or your school will pick a country of their choice for another topic (Our school chose USA history, but we could choose, Russia, Germany, China and other major places).
Not sure as to whether Sixthform wouldn't take IGCSE English language...I wouldn't believe it though. Normally IGCSE is more respected world wide than GCSE, because it's international (duh), and CIE is Cambridge university's exam board section - I believe Cambridge is well respected... Your teacher may be right, but I've never heard of anything like that in the past. I only heard CIE IGCSE English is easier but scientific subjects are harder...well...if only there were students who took I/GCSEs five times to test out different exam board lol