Flyway and liquibase together?
I would never recommend using both tools at the same time. In my experience, even only one of them causes conflicts/collisions from time to time in a big distributed environments(over 5 teams with access to the same DB).
I will also give you a couple of pros and cons when it comes to running these tools in projects with big, distributed teams:
FlyWay:
Cons: Very strict when it comes to migration files changes. If someone checked in their migration file, it is not recommended to change it. It's like using force push in git in shared projects. Changing a migration(either its content or the file's name) will cause a migration failure on every machine that had the previous version of the file. The whole migration pack will need to be run from scratch. In some cases it can take a lot of time.
Pros: Well, what was described in Cons will, at the same time, build up a level of discipline. It might be a reasonable restriction when talking about introducing simultaneous changes by several teams to a production-running application.
Liquibase:
Cons: With a couple of tweaks should allow you to change the existing(applied) migrations. While it can be considered as a benefit, with a lot of people working on the same codebase, extra caution should be exercised. Flexibility comes at a price. It's easier to introduce some "regression" or inconsistency when such "git force push" style of changes is allowed for distributed projects.
Pros: More configurable and more flexible. Might include solutions for NoSql in the future. A couple of useful plugins(hibernate integration, for example).
A small correction, before I answer question. The assumption
Liquibase seems to have everything Flyway has
isn't correct. Flyway shines when it comes to parsing SQL. You can use unmodified SQL files generated by your native tools containing all kinds of complexity like PL/SQL packages and procedures, MySQL delimiter changes, T-SQL, PostgreSQL procedures, ... With Liquibase you would have to split these in individual statements, add extra comments to the SQL files, ...
The beauty of being able to use your SQL files as-is is that you avoid lock-in. You can take your existing SQL files, start using Flyway with minimal investment and moved away later if it doesn't suit your needs anymore. Not so with Liquibase.
Also the issue of down migrations (think of them as compensating transactions, not rollbacks) is really something that sounds great in theory, but that is almost never needed in practice. See this old documentation page¹.
However when it comes down to using one or both, I certainly agree with SteveDonie (Liquibase team member) that using just one instead of the both together is almost always the better choice.
Disclaimer: I am Flyway's creator
¹ Though Flyway does support undo migrations nowadays, by reading the old documentation you'll understand the point Axel Fontaine is trying to make.