The obvious, out-of-universe answer to this question is that each regeneration shown in the early TV show was an example of the visual special-effects of the day. The show has spanned so many decades it is no wonder that the SFX have improved. The newer show since 2005 has also seen improvements in SFX over the seasons, but they appear to have tried to bring some consistency to the visual appearance of regenerations, especially after introducing the concept of 'regeneration energy'. This is the golden energy seen emanating from The Doctor's body before a regeneration before the fiery explosion of the actual regeneration.
'Twice Upon A Time' attempted to address the disparity between old-style regenerations and the new look by faithfully recreating the very first regeneration scene but retconned the account with glimpses of golden regeneration energy before it took place. It wouldn't be difficult for writers to explain away other the look of other past regenerations. The 6th regeneration did seem to show some kind of energy being emitted.
Don't forget also that some early regenerations were described as being "different". For a start, the second regeneration (2nd Doctor to 3rd Doctor) was not actually shown on TV. The series ended with the 2nd Doctor spiralling into an abyss but he never actually changed. The first time we saw the Third Doctor he had already regenerated, and actually a Doctor Who annual contained a story about the 2nd Doctor after the conclusion of his final TV serial which occurs on earth before his regeneration kicks in. Many consider this to be canonical.
Other "different" regenerations include that of the 4th Doctor, who "prepared" for his regeneration in advance and his new form was apparently contained in the form of The Watcher. The 5th Doctor's regeneration was also "different" (his final words are "feels different this time") and instead of seeing him regenerate, we see what is going through his mind as he does. The 7th Doctor's regeneration is also different, as he was "dead" when it happened.
Having already retconned the 1st regeneration and considering the facts that the 2nd, 4th, 5th and 7th regenerations were "different" in various ways, and that the 6th did look like regeneration energy (just not golden) we only really have to look critically at the 3rd. Which isn't so bad.