The Deluxe can handle the same things as Home and Business. The latter provides more help and guidance in regards to self-employed business, such as home office expenses, etc., but both editions prepare the same forms.
Have you installed all the latest updates since installing Deluxe, and have you restarted your Mac? If not, try that to see if it makes a difference.
I'll see if I can get @ macuser_22 to make a suggestion as to why it may be crashing.
If you end up needing to phone TurboTax Support, they are closed for today, but tomorrow they will be open from 5AM Pacific to 9PM (8AM-12 Midnight Eastern) due to the filing deadline.
You can use the form at the link below to schedule a call back, or it may provide a number.
Where the form asks what product you are using, be sure in the dropdown menu to indicate "CD/download" and the proper operating system, then indicate which Edition.
https://support.turbotax.intuit.com/contact
