Although, I use exactly your desktop pattern on my phone. Go anywhere there is a search bar (they're all over on Android), and search "wikipedia foobar" and go straight to the first wikipedia hit. Works better than wikipedia's own search usually.
And their mobile site is actually pretty nice. I like it at least. I'll check out the app though.
One interface feature I like with the app is within-article navigation: if you swipe inwards from the right edge, you pull out a table of contents, and can easily jump to article sections by tapping one. This is useful enough that I find myself unintentionally trying to do it in mobile Firefox, hoping I can jump around a blog post or documentation's headings that way (I wonder if mobile FF could implement this? do enough pages use HTML headings in a semantically meaningful way?).
This is more a stylesheet choice, but the app also more aggressively collapses things other than the main article text, like infoboxes and tables. On the mobile web view I find I have to scroll down too much to get past big infoboxes and such.
On slower phones and slower data connections it's also speedier. Especially on longer pages and pages with more non-text stuff, my phone has a noticeable pause to render the page after it loads, while in the app it's nearly instant. The data transfer via the app is also low enough that it's usable even on slow connections (I'm semi-frequently on T-mobile's free global roaming, which is rate-limited to 2g speeds, ~128 kbps). Since the interface is already preloaded, all it needs to do to load an article is grab the article text through the MediaWiki API, which is usually in the range of 2-20kb. It then lazy-loads images later (which you can disable if you really want to be lean on data).