As Alexey and pommes already said, switching from 2-tier to 3-tier architecture changes nothing in terms of SQL blocks/deadlocks.
But, if we are more specifically talking about migrating from NAV 2009 to NAV 2013, there are several other changes besides 3-tier architecture, that were directly focused at the SQL blocking issue.
One of them is the redesign of sales and purchase posting routines to decrease significantly the period when G/L Entry table is locked:
https://blogs.msdn.microsoft.com/nav/2012/10/17/gl-entry-table-locking-redesign-in-microsoft-dynamics-nav-2013/
Another important change is switch of the isolation level used for pessimistic concurrency (LOCKTABLE, etc.) from SERIALIZABLE to REPEATABLE READ. Though it is possible to make this change for NAV 2009 as well, in NAV 2013 it is the default option. This change directly reduces the probability of blocks/deadlocks. You may read more about this change here:
https://blogs.msdn.microsoft.com/nav/2011/05/12/microsoft-dynamics-nav-changes-by-version/
Besides that, the whole data access stack was rewritten and all native-db-compatible code was thrown out. That allowed to optimize for SQL server (as opposed to native DB architecture), introduce more effective queries and data caching. While it doesn't directly influence blocks, it means faster data manipulation and, as a result, locks are held for less amount of time.
https://msdn.microsoft.com/en-us/library/hh169480(v=nav.70).aspx
Together with some other features of background posting, these changes could result in NAV 2013 being more effective in terms of SQL locks as compared to NAV 2009.