Having just scoured the internet looking for an answer to a similar problem myself I can tell you how I finally got something similar working:

Instinct told me to try the

attrs="{'invisible':[('customer','!=',True)]}"

approach too. But, I believe attrs don't work to stop the column name itself from appearing in a tree view (works only on the values of each row).

Instead, you need to overwrite the fields_view_get method from within your res_partner python code, which will allow you to change the viability of each column by checking the context. In my case I was looking at Supplier vs Customer invoices, so I checked for the context 'type' being 'out_invoice'/'in_invoice'. In your case I believe customers vs suppliers are given a context value, something like "default_customer" and "default_supplier".

Anyway, in the end you want to remove the attrs element from you xml view and then add something like this to the python code:

  from lxml import etree

  def fields_view_get(self, cr, uid, view_id=None, view_type=False, context=None, toolbar=False, submenu=False):

    if context is None:
        context = {}

    res = super(res_partner,self).fields_view_get(cr, uid, view_id=view_id, view_type=view_type, context=context, toolbar=toolbar, submenu=submenu)

    doc = etree.XML(res['arch'])

    if view_type == 'tree':
        if context.get('default_customer', '0') in ('1'):
            for node in doc.xpath("//field[@name='n_supplier']"):
                doc.remove(node)
        if context.get('default_supplier', '0') in ('1'):
            for node in doc.xpath("//field[@name='n_client']"):
                doc.remove(node)

        res['arch'] = etree.tostring(doc)
    return res

I can't guarantee this will work straight off as I havn't tested it for your case, you might need to tweak some values above. Nor can I guarantee this is the best way to achieve this. But I can say very similar code is working perfectly for me in my situation.

Hope that helps :)