One clue might be the fact that you're using webmail on the desktop. That allows the ISP more control over what happens to your mail. When you use POP3 or IMAP access to a mailbox (as the iPad does) the ISP in some cases assumes that you will sort out the issues surrounding junk and spam mail yourself. As for Outlook doing something different again... no idea I'm afraid but it wouldn't surprise me if Microsoft has taken it upon itself to filter some stuff out for you.
I'm sure that there are options out there to filter spam in your iPad inbox but I'm not familiar with them. My approach is to forward them to Spamcop so that the ISPs that send it out are notified. It has not removed all spam but reduced it by a big amount. The way I see it is that a spamfilter doesn't solve the issue, just ensures that you don't notice it too much.