In my opinion, the IELTS test is a much broader test which suits candidates from all language abilities ranging from beginners all the way to proficient users. If you decide to take the IELTS because you wish to study at an undergraduate level you should consider the Academic IELTS. However, the CAE is much more level specific test suitable for candidates with very good language skills, for this reason it could be overwhelming for modest users. This test should be preceded by FCE (First Certificate in English) which corresponds to intermediate level, otherwise modest language users may find very challenging attempting an advanced exam such as CAE.
The two tests use different band scores
The table below shows how they compare:
IELTS band score CAE score CEFR level
8 80 C2
7.5 74 C1
7 67 C1
6.5 58 C1
6 52 B2
5.5 47 B2
5 41 B2
For more information visit: http://www.cambridgeenglish.org/exams/advanced/results/ielts-score/
Both tests are widely excepted by UK universities and employers and aim to assess language skills.
If you require specific information regarding entry requirements, you should consult the university you wish to attend but as a general guide you should be at at least 7/67/C1 User or above.
If you have any specific questions, please post here.