Is "nowadays" the same as "today"?

I think you were on the right track when you mentioned it might be a question of register: to me, nowadays is old-fashioned in a sort of folksy way, rather than a "we're not that exact anymore" archaic way that would actually make a word more formal. But that's just my gut feeling, no support whatsoever.

nowadays   (adverb)
at the present day; in these times: Few people do their laundry by hand nowadays.

today   (adverb)
1. on this present day: I will do it today.
2. at the present time; in these days: Today you seldom see horses.

So the second meaning of "today" is more-or-less identical to "nowadays", but that's not the meaning you want when you're trying to say you approve of something. Today is the bright, shiny, new day of opportunity; nowadays is the faded shadow of yesteryear. As Prof. Lawler said, "nowadays is often used to disparage present conditions in contrast to the past."

Oops, forgot to address the compound word part of your question. I've certainly never considered "nowadays" to be a compound of anything, because if you subtract the obvious "now" part, you're left with "adays", which doesn't look like a word. Most compounds have two parts, so it would be a bit of stretch to break it down as now + a + days, though I suppose that's possible, and I'm sure you're not the only person who has ever done so.

I agree with your recommendation. While it's not technically an error, in my judgement "Nowadays" will probably be perceived as a colloquialism, and therefore sounds less erudite.