The most attractive thing about any agile methodology is that the processes are am embodiment of values. What makes agile agile is the ability to change those processes if and when doing is what's best for the project.
Scrum, XP, and Lean all have their own ways of doing things - but the adoption of those practices doesn't embody agility.
For example, we are using the scrum methodology. This means designated sprints, daily stand-ups, planning, and retrospectives. But these aren't what makes us agile. It's the Scrum values - commitment, openness, courage, respect, and focus - that makes us agile.
The values that the different agile methodologies hold are also able to be utilised without adoption of the practices. The idea of seeing the whole is a value of lean, but it's just as useful a value to hold to while doing scrum.
The advantage of values is being able to respond and change to difficult situations without falling back on the process. Values are our metric by which change is guided and assessed. They are the why of the processes that allow us to know what those processes are for.
Processes without the values can be followed and confer the same advantages as a team who have internalised the values. But knowing the processes without the values makes it harder to realise those advantages when the processes become burdensome or sub-optimal. An agile team has the ability to better utilise the processes than one who follow the processes without the values guiding them.