Windows Phone 7 had Internet Explorer (IE) built-in. It was primarily a modified build of IE7 (with some bits from IE8). It offered a pretty fluid, smooth browsing experience with decent speeds. It lacked Flash & HTML5 support. Later, Microsoft introduced IE9 for Windows Phone 7.5 in conjunction with the release of IE 9 on the desktop. Mango with much better HTML5 support built-in. The performance & standards support was vastly improved over the predecessing version of IE in Windows Phone 7.
Performance-wise, Microsoft showed IE10 on Windows Phone 8 out-perform the Samsung Galaxy S III, HTC One S & iPhone 4S on iOS 6 Beta on a SunSpider test.
The Metro version of IE10 in Windows 8 has limited Flash support. Whether IE10 in Windows Phone 8 will have similar Flash support or not is still unclear. But, it is safe to assume that it will be there. So overall, IE10 in Windows Phone 8 is well ahead of the current smartphone browser situation.