I wanted to chime in on a issue I've had with outlook premium. Two issues, in fact, but one quite severe.
In essence, this is a consumer version of hosted exchange via Exchange Online P1 ($4/mo) which is slowly being superceeded by Office 365 Small Business Essentials ($6/mo) to include 1TB of OneDrive as Microsoft tries to push that product into their ecosystem presumably to offload large attachments from Exchange.
Anyway, that said, Outlook.com premium is a great alternative for a SINGLE user, whether they desire their own domain or not, because it effectively gives them Outlook.com/Hotmail/MSN Exchange access like everyone else gets for free, but with 50GB or email, no ad's, and a mildly neutered Office365 corporate mail interface (outlook web access, some admin controls, etc.)
It does not give you powershell access (so no way to increase attachment limits to 150MB like on other hosted exchange plans) and it does not give you a true admin control panel. Everything is dumbed down.
The issue I want to bring up is CPU time. Without powershell access I can't check to see what actual processing power there is, but it is bad, and actually seems to get worse over time indicating throttling or allotted CPU cycles per week/month.
Where this becomes a problem is during an initial seed of your email. If you are moving from POP mail and have a decent sized PST file, say 10-20GB, it will seed at about 5 messages per minute or 50kb per minute. The initial seed moves fast and falls off after 1GB, indicating a grace period for burst uploading, but they clearly don't want people using this to seed a large email database. Which is unfortunate because it seems the natural candidate for this service would be someone switching over from some crap email service like Comcast or Yahoo who have built a large POP-based PST over the years and want hosted email.
Also unfortunately missing from Outlook.com Premium opposed to all other hosted exchange services like P1 all the way through E5, and all Office365 plans, is the ability to migrate from a variety of services within the admin control panel because the traditional admin interface is missing. The traditional hosted exchange admin control panel offered with every other hosted exchange plan I've ever seen from Microsoft has a migration tab that allows you to select gmail (where the interface logs into gmail, makes it a trusted app, and can migrate email, calendar and contacts automatically) and a variety of other services such as Yahoo, Hotmail/Outlook (if migrating from one outlook.com account to a new one!) and most importantly, a PST file! I can't tell you what an oversight it is they left this out. Making migration easy should have been the PRIMARY GOAL of Outlook.com Premium, but instead they didn't even include a way to do it, encouraging people to half ass it with a forwarding system from their old email address(s) and/or seed their OST via migrated PST.
Outlook.com Premium demonstrates how clueless Microsoft is with the consumer cloud computing segment. They are kinds in the corporate and enterprise sector, but for a mild discount, Outlook.com just isn't worth it even for $20 a year. For $48 a year, you get a real hosted exchange account with a real admin control panel and no neutering. The fact that migrating will be easier and faster will inevitably make it CHEAPER if you are paying someone to help you set it up. If you need a custom domain, go daddy sells them for $10 a year and is a Microsoft partner so you can actually purchase it directly through the Office365 or hosted exchange setup process.
Do not buy outlook.com Premium. There is a lot of little issues I left out because I could write a book on what a poor product it is but I'll leave you with one more:if you are using outlook 2007 or 2010, opposed to 2013 or 2016, any mail you send from Outlook 2007/2010 will not send from your custom domain even if selected from the "From" account. It will always default back to the initial Outlook.com address. iPhone and android don't have this issue, nor does the outlook web interface. The problem stems from Outlook 2007/2010 missing the address translation layer that Exchange 2016 uses and Microsoft has no plans to add it to Outlook 2007/2010 as they are legacy products no longer supported. Therefore Outlook 2007/2010 cannot take advantage of the secondary domain(s) linked to an email address on an Exchange 2016 server. This issue does NOT exist on a hosted exchange account using P1 up through E5 or any Office365 product because they give you an admin control panel allowing you to eliminate the onmicrosoft.com domain, hence making your custom domain the only domain, and therefore the primary domain. Setting the "reply to" domain account under Outlook.com Premium doesn't do the same thing, because Outlook.com will always be the primary domain to Outlook 2007/2010.
A real problem for legacy users who prefer Outlook's older interface predating "Metro UI"
But as I said, I could go on. Just too many problems with Outlook.com Premium and migration is at the forefront of them.