Both GATE and IIT JEE are difficult. The selection rate is comparably less for IIT JEE, as millions of students take the examination each year.
In GATE, you will appear for your branch of study, so it is easier in that respect. But scoring well is difficult, especially for branches like CSE, EEE, etc.
In terms of syllabus, IIT JEE covers more subjects. Although the number of subjects is less in GATE, you need to have in-depth knowledge to score under 1000.
Overall, GATE has a less competitive environment, but it has its fair share of difficulties.
GATE and IIT JEE, both examinations are difficult and come with different challenges.
JEEs are exams that are conducted to select students who want admission to IITs or NITs. GATE, on the other hand, is used to select students who want to do master's or gain a job in PSUs.
IIT JEE and GATE are very different exams. JEE is an undergraduate exam, whereas GATE is a graduate exam.
Comparison:
The competition for JEE is slightly higher than GATE since JEE is based on the same syllabus. In GATE, you have an option to choose between several papers. Although there is less competition in the GATE, if you do not have a rank under 1000, then it is likely that you will not get selected for PSUs or IITs.
Almost everyone in the science branch will attempt IIT JEE after their schooling. GATE is only attempted by those who are interested in researching or to get high-level jobs in PSUs.
You will need more revision for GATE, whereas JEE is more about logic- application.
For GATE, Final year students will find it difficult to prepare since the syllabus is a lot more than their courses in college. IIT JEE syllabus is closely related to the 10+1 and 10+2 syllabus. This makes it easier for students appearing in board exams to prepare for IIT JEE
JEE only the rank is considered for admission. However, for GATE, rank is not considered, instead, a normalized GATE score is chosen as the criteria which can be quite tricky. Further, different IITs might have their own separate exam and interview rounds. You will be able to secure admission into IITs only after clearing these rounds as well.