I'd really like a 15 myself - but the 16-45 is quite close in range and decently lightweight. Both are f/4 for that matter, and the 16-45 is well regarded and much easier on the budget. I do not doubt the 15 is superior in IQ, but you take what you can afford.
You can grab a 16-45, see what you think and re-sell for no more than a modest "rental fee". I'm on my 2nd 16-45 and I'm thinking it is close enough to 15 for me. If I had the 10-20 I suspect I would do the trade you are considering - but I have never owned an ultra-wide zoom so I cannot prove it