Why Ekalaivan was a better archer than Arjun is a long discussed topic. I guess, science is answering this question now. It is proved that the online learners / distance learners are better self-regulated than the class-room or in-person students. Ekalaivan was probably the first ever distance learner! Like many other distance learners, Ekalaivan also was learning for his own pleasure & need and not out of compulsion by a parent or someone. When one is intrinsically motivated like that, they are better self-regulated and hence better learners and better performers!
There is an additional possible explanation! Hawthorne Effect! For Arjun, Drona was in physical form. He could differentiate between the physical presence and absence easily. He may have practiced / done right things only when Drona was around. But, for Ekalaivan, Drona was not a physical form; he was a virtual form that is present always, a feeling that is constantly existing. There is no possibility of absence of the guru for him. The only way he could have survived this feeling was by practicing all the time, behaving himself, eating right always. A case of perceived attention improving productivity and performance!!!! His feeling for his guru probably was so intense that he did not need any reiteration of the idea that his guru is next to him always…
It is interesting that ancient India considered the guru as same as God! They also believed that the great gurus can manifest themselves anywhere! Application of Hawthorne effect I feel :-) :-) How many teachers qualify to be at that level is a different question though! But if we think carefully, Drona himself was not good enough to be treated as God… he lied, was partial and violated war ethics. It looks like, it is the disciple's feeling for the guru mattered more than the quality of the guru!! However, we should remember that, the guru should be of good quality otherwise the student will end up learning wrong things or the overall outcome will go in vain… like in the case of Ekalaivan.
Drona was the guru for Pandavas and Kauravas too. If we compare their performance with Ekalaivan, they were poorer. But within themselves, Pandavas were better… that is probably because, the Pandavas had access to their other great guru - Krishna. One can see the influence of the "Hawthorne effect" easily with Krishna. Pandavas kept Krishna out on purpose whenever they committed mistakes; they made explicit requests to him to stay away mentally! For example, Yudhisthira pleaded Krishna to be away when gambled / played the fatal game; he went on to make all ugly mistakes when he kept his guru away mentally. Not only that, before they set out to the war, the pandavas shared their most dreaded secrets with one another and Krishna to create the bonding once again with their guru.
Kaurvas did not have this feeling for their guru Drona. They did not keep him at their heart! Interestingly, Drona did not keep his best student Ekalaivan at his side! In other words, Drona was not that good a teacher as Krishna. His students did not consider him as omnipresent; he deceived the only student who considered him as omnipresent! Krishna's disciples kept him close to their heart, treated him as God and felt his presence always. Krishna too stepped down or up to any level for them- he accepted rather volunteered to be a charioteer to his student, a messenger on behalf of his students, astrologer for his students; he never let them down! We all know the result of such an alliance!!