を・で Nuance difference?

まいあさ、こえん　xx　さんぽします。 I expected xx=で but the answer is given as を。 I've seen suggestions there is a different nuance, one being more purposeful, deliberate than the other........ can anyone elaborate? Oh and さんぽします or さんぽをします? I see both. As spoken, hard to tell apart, it can sound like さんぽうします..... (There are other examples where を comes & goes before する where the noun doesnt end in an o sound & its more obvious, but I cant bring another one to miind.)

For the second sentence, both さんぽします and さんぽをします are correct as the particle を can generally be omitted. As for the first problem, I don't really have an idea how to explain it, but I can translate in english what each may literally mean: まいあさ、こうえんでさんぽします -> I take strolls in the park every morning まいあさ、こうえんをさんぽします -> Every morning, I stroll the park. Using を, the sentence takes more of a rigid nuance.

Thanks. Since asking here, Ive asked some of my Japanese native speakering contacts re で・を They all agree it has a different nuance; and none of them can really explain what it is! There is a sort of suggestion that using を makes it more purposeful, deliberate, for a reason, which I guess is roughly your 'rigid' nuance.

Yeah, it's really hard to explain this kind of thing...think of situations when someone sais that your way of speaking is really: "katai". You'll get used to the difference between them as time passes and as you exercise more :)