Zapdos dominated in many catagories in GSC,Special Attacking,Electric types,etc. While that is not true for suicune in gen 3(ADV)And while Suicune may be good its just meh in its meta.W/ reliable recovery it would probaly dominate ADV but its that and "locked movepool" that stop suicune from bieng good.Also Zapdos actualy was quite a dominate force,The Meta wouldent be the same but it wouldent be too shifted if suicune left iirc.but if Zapdos or Snorlax left GSC it would shift majorly iirc.
Secondly, locked movepool? Last time I checked the only 2 moves that are mandatory on a Cune set were Calm Mind and a STAB move (a trait that Jirachi, a renowned "versatile" pokemon shares)- the rest of it's set can be a number of things- Rest/Roar, Rest/Ice Beam, Resttalk, Sub/Ice Beam, or even Ice Beam/HP Electric. That's more than enough options to pose a multidimensional threat, and they all require different methods to overcome.
You are right that removing Cune would have less effect than removing GSC Zap, but not for the reasons you think. As I already said, Cune has many viable sets that it can run, and they perform and threaten in different ways. In fact, between its sets it can get past any pokemon in the game. Zapdos, while being amazing, does not have that luxury. Like I said earlier, the comparison doesn't apply. It has no way around Raikou (unless extreme parahax), and thus it probably owes its high usage to Zapdos' existence. Suicune has sets for Blissey, for Celebi, for Zapdos, for Regice, for Gyarados... can you see the problem? Theres not a way to beat all Cune sets with one poke, and things that do give most Cune sets trouble (Zapdos, CMBlissey, Raikou) will run those sets regardless because they're so effective in other common scenarios. If any change were to happen, it'd probably just be the things that Cune walls getting more prevalent, such as TTar, Flygon, Mence, Aero, and Pert. Especially Pert.