You shouldn't be running them both at the same time, they are both antivirus and you should only ever have one AV program installed otherwise they can conflict with each other (and it will cause a huge drain on system resources)
as for suggesting which to get rid of, it's a tough call, I've not used MSE but it has got some very good (independent) reviews in the AV community and Microsoft did throw a lot of money (and outside expertise) in getting it right after their onecare attempt at security was a joke!
(incidentaly ad-aware is anti spyware, which is different to anti-virus and you can have anti-spyware software installed at the same time, though I'd recommend malwarebytes instead of ad-aware)