紧迫 urgent; pressing; imminent:
急迫 urgent； pressing； imperative
I have analyzed many words relating to urgency, but this is the only pair I was not able to distinguish
I have a Chinese thesaurus dictionary (现代汉语同义词词典) . It does not compare 紧迫 with 急迫 directly but compares 紧迫 with 紧急 and 急迫 with 急切.
紧迫 is definitely much more widely used both in written and oral Chinese. It feels as if you can use 紧迫 to replace 急迫 and it is still fine but not vice versa.
About the comparison mentioned above, it is dauntingly long even for a native speaker. If you are interested, check it here https://pastebin.com/b8tGSeNF
紧迫 (tightly press) = pressing ; urgent
迫 (pressing/ forcing)
Example: 时间紧迫 (time is pressing)
紧急 (seriously hurry) = urgent; emergency
情况紧急 (situation is urgent)
紧急会议 (emergency meeting)
迫切 = (immediately pressing) = urgent
-切 (serious/ immediate)
切 in 迫切 is the same one in 切身 (immediate to oneself)
It is different from 切勿(seriously don't) and 切记(seriously / must remember)
1.截止日期迫切 (deadline is immediately /seriously pressing)
2.迫切进攻 (urgently attack)
急迫 is not a common term, it is a combination of 紧急 and 迫切 (紧急而迫切 pressing and urgent)
I'm a native Chinese, I'd say 紧迫 is describing things while 急迫 is describing people more.
However you could use 急迫 for describing things as well, but 紧迫 is more formal in such case. But one would never use 紧迫 for describing people.
1. 紧迫的任务 or 急迫的任务: An urgent task. #here 紧迫 is preferred
2. 他急迫的想回家: He want to go home urgently. #here 紧迫 can't displace 急迫