How will Phd guides treat students who are pursuing PHD under scholarships other than institute one?
The answer is based on my experience as faculty at a UK university (engineering).

Officially: There is no discrimination between institute or externally funded PhD students (either from the UK or their home country). There are strict rules and a logging and management system that ensures all students get the same number of guaranteed supervision hours.

Reality: Our school management actually is biased to support more students with international scholarships. The reason is that they bring a lot of money into the school directly through the huge amount of fees their scholarship pays.

Other info: Supervisors (incl. myself) tend to bias towards stronger students in the long-term (no matter their scholarship). When a student generates a lot of results and writes many high-quality papers, then I am inclined to support the student more than the minimum required (review papers, have more meetings, work more closely, etc.). 

The first 1-1.5 year I support weaker students slightly more than the “guaranteed” to give them a chance to catch up. If a student is weak after the first 1-1.5 year, then I tend to provide them with the minimum required supervision while spending more time with the stronger students.

The reasoning is that spending 100 hours extra with a strong student might lead to 3 strong journal publications while with a weak student 100 hours extra might lead to an average journal at best. Since my progression is heavily based on academic track record, it’s natural to bias towards the most beneficial use of my time. Note that these are extra hours in addition to the “guaranteed” by the regulations supervision.