The presence of Apple’s (AAPL) mobile devices on the Web surged this summer and early fall according to Net Applications and StatCounter, two leading mobile analytics services, although the two firms draw very different conclusions about where that leaves competing platforms.

Net Applications, which monitors hits on its 40,000 client sites and weighs the results based on population statistics, issued a report Monday that shows Apple’s iOS dominating the mobile Web with a 61.64% share, up 7 percentage points in October alone. Google’s (GOOG) Android — despite smartphone sales that long since overtook the iPhone’s — came in at less than 19%, only now passing Java ME.

StatCounter, based in Dublin, monitors more websites — 3 million as of June, according to its fact sheet — but does not weigh the results (“We simply publish the data as we record it”). In its latest snapshot of the Web, Nokia’s (NOK) Symbian still dominates despite its lame-duck status, with iOS and Android playing catch-up. But StatCounter too registers an Apple surge, with iOS’ Web share rising 33.6% over the past four months. Android is also rising in StatCounter’s charts, but at a diminished pace.

A key factor driving Apple’s Web presence, of course, is that iOS runs on three popular devices — iPhone, iPad and iPod touch — that invite casual Web browsing. There is no Android equivalent of the iPod touch, and although there are multiple Android tablets — and more about to hit the market — none has yet to take off.

Both firms show Nokia’s Symbian and Research in Motion’s (RIMM) BlackBerry OS rapidly losing share. But how StatCounter can register a 29% share for Symbian where NetApplications sees less than 3.5% is a mystery to me.

[UPDATE: StatCounter does not count tablets in its iOS total, which explains some of the differences between the two services, but not the Symbian discrepancy.]