A funded PhD would be awesome (rare as they are) but self funded looks like you get more say in the direction and methods of your research.

Any thoughts on this?

There are few positives to self-funding. I'd have thought that the direction and methods of the research is driven by the research, not the funding situation.

I think it depends on the situation, but I've heard you do have more flexibility, but also that can mean less supervision direction. Supervisors will jump at the chance to take a self-funded student but if your topic isn't exactly what they do it may be difficult for them to guide you as much, if that makes sense? It'll completely depend on individual circumstances though.

I think this also largely depends on the source/type of funding... if your funding comes from a specific project then yes, you will possibly have to work within more constraints, e.g. your external partners may wish you to do the funding using X tool even though you'd prefer to use Y.

My funding was a Doctoral Training Account studentship - as a result, I could do whatever I wanted as there were no external partners or other project constraints. That can be a blessing, and also a curse!

This blanket statement of "self funded PhD students have more freedom" is simply not true... be careful about overgeneralising*.

*A good lesson for your research as well!

Depends on
(a) your field e.g. funded or not, science PhD students will rarely have free reign to choose any topic as there are usually constraints on the available equipment, samples, databases etc. Arts and humanities students are generally more able to put forward their own proposal and tend to do so whether funded or not. Also worth bearing in mind that science/engineering topics requiring experimental lab work will be incredibly costly (one may need to cover lab costs of up to £1000/month depending on the type of work).

(b) your reasons for doing a PhD. If your primary aim is to immerse yourself in a topic that fascinates you and you're not fussed what happens afterwards then self funding may be an optimal way to increase your control over your topic. If, however, your primary aim is a career in academia then be aware that a PhD (funded or not) is an investment with a very poor rate of return, thus a self funded PhD can be incredibly costly with little benefit.

Also worth bearing in mind that PhD theses rarely end up up looking like how anyone imagined they would at the beginning of the process. Also, the steer one gets from a supervisor in a different direction is often there for a reason (supervisors aren't always right but if their vision from a project differs from your own you need to think very carefully before ploughing ahead regardless).