What's is new in Mail app in Lion compared to Mail app in Leopard Snow?
The Apple Web site on Mail in Lion summarizes the most important new features. If it's "really any better" or not, depends entirely on your personal taste: I do like Mail.app's new list view where the list appears as a side bar, with chunks of message text in addition to the subject/sender information. You can further unclutter the interface by hiding the Mailboxes tree when you don't need it.

The search feature has also got better: things that used to require "Smart Mailboxes" (multi-condition filters) you can now do with a quick search in the search bar. Apple also seems to have stolen some good ideas from Google Mail – like Thread view, which is activated in Mail for Lion by default, and groups together messages that belong to the same thread. A thread shows up only once in the message list, showing the number of messages. It's very convenient to move/delete a whole thread in this way.
Also a neat feature copied from Google: the quoted text of original emails in replies is hidden by default, but you can unfold it by clicking "show more" (with a nice visual effect of unfolding paper). 

However, if you love Thunderbird's special features, Mail.app is probably not for you. It's missing the Thunderbird's superb Tabs feature, i.e. you can only view one email folder / search result at a time (this might actually bring me to consider switching to Thunderbird again).

Personally, I like Mail.app because it's much better integrated with the other OS X apps I use, such as Address Book, iCal and iChat. Example: I get an email from a colleague, and if she's currently online in GoogleTalk/Jabber or Bonjour (local network chat), a green dot appears next to her name directly in Mail. Can't have that with Thunderbird... Other example: dates, times, addresses and phone numbers are recognized automatically in email text and can be added in one click as iCal event or to complete an Address Book entry. Also, I'm not sure whether Thunderbird's email database is indexed and searchable with Spotlight. Wouldn't want to miss this feature: searching for an email by subject or even message text without opening Mail in the first place.