Who's sage Vashishta's Best Student (other than the sons of King Dasharatha)?
If we are leaving Rama out of contention, the most accomplished of Brahmarishi Vasishth's students would be Harishchandra. SECTION XII of Lokapala Sabhakhayana Parva of Book 2 of Mahabharat mentions Harishchandra as the only earthly king who finds a place in the assembly of gods:
The Brahmanas gratified with various kinds of food and enjoyable articles, given away unto them to the extent of their desires, and with the heaps of jewels distributed amongst them, began to say,--King Harischandra is superior to all kings in energy and renown.--And know, O monarch, O bull of the Bharata race, it was for this reason that Harischandra shone more brightly than thousands of other kings. The powerful Harischandra having concluded his great sacrifice, became installed, O king, in the sovereignty of the earth and looked resplendent on his throne.
In these verses Devarishi Narad gives Pandu's message to his eldest son asking him to follow the footsteps of Harishchandra and perform the Rajsuya Yagya so that even he can attain heaven:
O king of the Kuru race, O son of Kunti, thy father Pandu, beholding the good fortune of Harischandra and wondering much thereat, hath told thee something. Knowing that I was coming to the world of men, he bowed unto me and said,--Thou shouldst tell Yudhishthira, O Rishi, that he can subjugate the whole Earth inasmuch as his brothers are all obedient to him. And having done this let him commence the grand sacrifice called Rajasuya. He is my son; if he performeth that sacrifice, I may, like Harischandra, soon attain to the region of Indra, and there in his Sabha pass countless years in continuous joy.
Bhishma also mentions to Yuddhishthir in Anushasan Parva Section CXV:
Do thou always speak the truth. Never speak an untruth. Truth is an eternal duty. **It is by truth that Harischandra roves through heaven like a second Chandramas. **
Since everybody knows about the trials he was made to endure by Brahmarishi Vishwamitra, I am not going to mention them but what happened afterwards clearly shows the regard Vasishth had for his protege. The Markandeya Puran gives the details of his whole story and also mentions what happened after he had proved himself worthy:
Dharma said- 'O king! You have satisfied me with your merits like patience, endurance, truthfulness etc.' Indra said- 'Harishchandra, you are very fortunate. You have won our hearts along with your wife and son. You have even won the heaven with your action. I invite you to stay in heaven along with your wife and son.'
Brahmarishi Vasishth had been undergoing a penance at the time Harishchandra was undergoing these adversities and when he came to know what Vishwamitra had put his protege to, he cursed him to become a bird and they had a huge fight:
The birds say- O great sage Jaimini! When, King Harishchandra attained his heavenly abode, their family priest, sage Vashishta re-emerged from water. He came to know about the entire development. He was angry at Vishwamitra's stubbornness. He at once cursed Vishwamitra to become a stork. On the other hand Vishwamitra cursed Vashishta to become a partridge. Thus both of them turned into birds and began to fight. Their fight caused great panic all around. At last accompanied by the deities, Brahma himself arrived at the scene and dissuaded the birds from fighting. But Brahma could not convince them and they continued to fight. Brahma then destroyed their avian appearances and both the sages regained their original form. Their enemity too ended at the same time. Brahma explained to them that Vishwamitra had not done any harm to Harishchandra. In fact he had felicitated Harishchandra's ascend to the heaven. Both the sages felt ashamed and they embraced each other before leaving for their respective hermitages.
We don't see Brahmarishi Vasishth fighting on behalf of any of his other pupils!
So, more than Shakti/Shaktri who frequently lost his cool and first cursed Harishchandra's father Satyavarat and then king Kalmashpada, I would say that according to the scriptures, Raja Harishchandra was better than all other kings and monarchs.