useful-objects | object must be useful immediately upon instantiation

If you can, go with Symfony 4.0

A lot of times with Symfony, when we reach the brink of a new major version like 4.0 what you'll find more often than not is that the previous last minor version, in this 3.4 is mostly compatible with it, just that deprecated features are removed.

In other words, the biggest change between 3.4 and 4.0 is that any features marked as deprecated in 3.4 won't work in 4.0.

Whereas the major difference between 3.0 and 3.4 is all the new goodies that convinced the team to leap from 3.4 to 4.0

There are a few minor stuff but this is the biggest difference in my opinion, so go with 4.0 which also has the added benefit of saving you another leap when 5.0 comes out end of next year.

All the best!

Allow me to respond to the other answer that has been surprisingly more popular.

If the question is "Which Symfony version (3.0 or 4.0) is closer to 3.4?" I am genuinely surprised that anyone would say 3.0, genuinely.

Symfony 4 is Symfony 3.4 without support for any deprecated features. - that is the main point here.

Symfony 3.0 is Symfony 2.8 without support for any deprecated features.

Don't take my word for it, check out the official blog on the parity https://symfony.com/blog/category/living-on-the-edge

Notice how 3.4 and 4.0 are grouped, as well as 2.8 and 3.0.

The closest to 3.4 is 4.0, why? You can safely downgrade from 4.0 to 3.4 without issues (unless with 3rd party bundles), you can also safely upgrade from 3.0 to 3.4 but mostly with deprecation notices everywhere not to mention your code lacks the features introduced in 3.1, 3.2 and 3.3. I'm baffled why some would think the closest to 3.4 is 4 minor versions back. But they gave reasons so I'll briefly counter them.

1. Semantic Versioning really is just numbers, what's important are which feature set is closest to 3.4, 4.0 or 3.0?
2. Symfony flex is not Symfony. In fact it is completely separate and my production app is using the latest Symfony 4 version without flex.

3. Perhaps the now chosen answer was not aware of this, but directory structure is totally optional, my aforementioned production app uses Symfony 3.4 directory structure in my Symfony 4.1.x backend. Just make sure composer.json is aware of your structure.

   "autoload": { "psr-4": { "AppBundle\": "src/AppBundle/" }, "classmap": [ "app/AppKernel.php", "app/AppCache.php" ] },

4. Symfony 4 advises against using bundles to organize your code, it's not set in stone, again just related to above, let composer know that your code is in src/AppBundle.

Actually, to conclude, most of the reasons stated to choose 3.0 are cosmetic, however, should you want to know which features are in 3.0 that are not in 3.4 take a look at the link I put, here it is again. https://symfony.com/blog/category/living-on-the-edge

In the end, it's people's opinion, and I'm happy to let the popular one carry the day even if it aint my own.

Good luck!