I cannot give a definitive answer to this question because it depends on a lot of things. So I will just give some remarks:
I am slightly skeptical of putting all of my passwords into a piece of software and having that single point of failure that can be accessed through the internet.
So I am! My password vault exists in 2 places: on my desktop and on my smartphone and it is never copied on a cloud folder: it is not a single point and only a previous successful attack could make it accessible through internet. What I mean here is that I use 2 defense lines: the file is not publicly available and its data is protected with a password and a strong encryption
... is more secure than writing your passwords down on paper
Passwords on a paper is generally considered as a really secure solution if the paper is then stored on a physical safe. It is still common for secrets for which loss of availability would have serious consequences on an organization: only few people (ideally only one person) use the secret on normal use cases, but if that person dies or is seriously injured, a backup allows the organization to give the secret to someone else.
... assuming you obfuscate them in some way?
Obfuscation is generally frowned upon when security is researched. You have not explained how you want to obfuscate so I cannot give an advice on it (nobody can). But you cannot do without revealing the secret, so you can only rely on your idea being original enough to prevent an attacker to guess it, whatever they can know about you. You are on your own at this point, but asking the question is a sign that you are not sure of it...