Good question with no single simple answer.
I used to be a big fan of Hibernate. Multiple projects, multiple years of experience.
Used to believe that any project should default to hibernate.
Today I am not so sure.
Hibernate (and JPA) is great for some things, especially early in the development cycle.
It is much faster to get to something working with Hibernate than it is with JDBC.
You get a lot of features for free - caching, optimistic locking and so on.
On the other hand it has some hidden costs. Hibernate is deceivingly simple when you start. Follow some tutorial, put some annotations on your class - and you've got yourself persistence. But it's not simple and to be able to write good code in it requires good understanding of both it's internal workings and database design. If you are just starting you may not be aware of some issues that may bite you later on, so here is an incomplete list.
Performance
The runtime performance is good enough, I have yet to see a situation where hibernate was the reason for poor performance in production. The problem is the startup performance and how it affects your unit tests time and development performance. When hibernate loads it analyzes all entities and does a lot of pre-caching - it can take about 5-10-15 seconds for a not very big application. So your 1 second unit test is going to take 11 secods now. Not fun.
Database Independency
It is very cool as long as you don't need to do some fine tuning on the database.
In-memory Session
For every transaction Hibernate will store an object in memory for every database row it "touches". It's a nice optimization when you are doing some simple data entry. If you need to process lots of objects for some reason though, it can seriously affect performance, unless you explicitly and carefully clean up the in-memory session on your own.
Cascades
Cascades allow you to simplify working with object graphs. For example if you have a root object and some children and you save root object, you can configure hibernate to save children as well. The problem starts when your object graph grow complex. Unless you are extremely careful and have a good understanding of what goes on internally, it's easy to mess this up. And when you do it is very hard to debug those problems.
Lazy Loading
Lazy Loading means that every time you load an object, hibernate will not load all it's related objects but instead will provide place holders which will be resolved as soon as you try to access them. Great optimization right? It is, except you need to be aware of this behaviour otherwise you will get cryptic errors. Google "LazyInitializationException" for an example. And be careful with performance. Depending on the order of how you load your objects and your object graph you may hit "n+1 selects problem". Google it for more information.
Schema Upgrades
Hibernate allows easy schema changes by just refactoring java code and restarting. It's great when you start. But then you release version one. And unless you want to loose your customers you need to provide them schema upgrade scripts. Which means no more simple refactoring as all schema changes must be done in SQL.
Views and Stored Procedures
Hibernate requires exclusive write access to the data it works with. Which means you can't really use views, stored procedures and triggers as those can cause changes to data with hibernate not aware of them. You can have some external processes writing data to the database in a separate transactions. But if you do, your cache will have invalid data. Which is one more thing to care about.
Single Threaded Sessions
Hibernate sessions are single threaded. Any object loaded through a session can only be accessed (including reading) from the same thread. This is acceptable for server side applications but might complicate things unnecessary if you are doing GUI based application.
I guess my point is that there are no free meals.
Hibernate is a good tool, but it's a complex tool, and it requires time to understand it properly. If you or your team members don't have such knowledge it might be simpler and faster to go with pure JDBC (or Spring JDBC) for a single application. On the other hand if you are willing to invest time into learning it (including learning by doing and debuging) than in the future you will be able to understand the tradeoffs better.