Short answer: in one-player, yes (although it's really just the advantage of saving training time/NP, not a real battling advantage). In two-player, no.
Long answer: In one-player, all you really need is HP and strength. You have the advantage of knowing every weapon each challenger carries and exactly how difficult they'll be to beat, so with a strategy involving a double-freeze (diamond dust/fiery gaze one round and a real freezer the next) and some reflectors or a 100% blocker like Ring of the Lost, a 200-booster can take down even a 650-booster. And if your strategy depends on him using a certain weapon at a certain time and he fails to, you can just withdraw and try again without penalty. Of course, defence helps, and probably makes it easier to beat harder opponents earlier (my defensively-minded friend took down the 125-boost Tekkitu when she had the 35 boosts, thanks to some dark-defending dual-duties), but it's not necessary.
In two-player, you can't withdraw. You can't count on a double-freeze, and if you flash a reflector, your opponent will switch to an unreflected weapon. If two pets with roughly equal weapon sets and the same strength and HP go up against each other, but one pet has a high defence boost and uses that to his advantage (while the other can't use shields at all), the defender is probably going to win.
Consider this fight I had a while ago, before I trained my defence. I had the 200 strength boost and 230-ish HP, and 43 defence. My opponent had the 200 strength boost, 230-ish HP, and the 350 defence boost. I could last a few rounds: in round 1, both people freeze and there's no real damage done (usually), so that's okay, and after that I could last one round using burrow, one using sink, one using my thick smoke bomb, and one using downsize. I could maybe get through another couple rounds by healing (although he could heal, too, so it was just prolonging the inevitable). But after that, I was totally stuck. I was out of defense abilities and items. And he had a ghostkershield that he could use over and over and over to stop good chunks of my attacks. He could last many more rounds than I could... so he won. And that's the way it goes. Defensive battlers are a nightmare for all-out offensively-minded people. And that's why I just spent a couple months bringing my strength and defence both (soon) to 250!
(Another note: it's bad enough if the opponent is using just a shield. It's even worse if they use dual duties! At least with a shield they're only using one weapon -- in lower-level battling let's say they're using a Scuzzys Comb and hitting you with 10 icons from that, but they're also using the Leaf Shield and they're sacrificing hitting you with more icons so they can defend a bunch of yours. If they're a dual-duty fan, they're smacking you with two weapons (let's say Golden Compass and Dusty Magic Broom, for a total of 17 icons) while also defending, and you're really toast.)
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