I've been an Illustrator user for a long time. But, given their ever growing leanings towards cloud based products, I've been evaluating Inkscape. As is usually the case, it's not as polished as its commercial brethren or quite as efficient, but for drawing touch screen graphics (which is also my primary use for it), it's good enough.
Here's a little test graphic I did as a trial run. It's twenty-something layers or so, with a lot of blurs, gradient fills, gradient masks and so forth. Inkscape was struggling a bit at the end, but this is generally far more complex than your typical touch screen graphics.