What may be the difference between the usage of チャンス and 機会 ?
Do really people say "これは機会だぜ！"? I doubt it…
While you do say "これはチャンスだ" to mean "it's now or never", "just do it!", "go for it!" and other once-in-a-life-time opportunities, I think that "機会" is a much more usual opportunity, less outstanding situations. You would use 機会 to say "Since everyone is here, this is the opportunity to discuss the frobnication of frobnickers", or "I had the opportunity to meet her mother at the local supermarket." Nothing to write home about, just a simple description of the situation.
Also, by チャンス being a word of foreign roots, and 機会 a compound word, it is likely that the former is more colloquial than the latter. I also wonder whether 機会 isn't, statistically speaking, used to refer about an event in the past, while チャンス would be used to talk about some opportunity still to take.
(If you say "これはアタックチャンスだ！" do not forget to clench your fist and wave it doing circular motions in front of you)
As pointed out, for your examples チャンス would be more suitable. Although it seems more natural to me to use 「が」or even 「こそ」.
Also, 機会 has nothing to do with past or present.
If you want to expand your vocabulary, there are lots of other options to use for "chance/opportunity", although the context may vary somewhat.