MSE features its real-time protection against malware and spyware, heuristic detection, e-mail attachments scanner and browsing protection. AntiVir will offer the same except e-mail scanner (this feature is available only in paid edition of AntiVir).
AntiVir also provides anti-phishing protection and Secure Start protection which is quite useful because any identified malware is removed before the system will continue to load. However, both programs do not offer web shield against rogue and malicious websites (unless the website will download or load content that is malicious).
MSE and AntiVir let you run a quick, full, single (via context menu) and custom scanning. You can customize the scanner of AntiVir to use normal or higher scanning process which means it can finish fast but will use more memory or use lower memory but the scan will take longer to finish. This option is not available in MSE. AntiVir has the option to run a boot records scan.