Instruction: Extract information from the supporting document to answer the given question.

Input:
Question: Why would I add this to my current DS413 rather then adding, for less money, a new DS414?
Document: - I would HIGHLY recommend pairing this system with the WD Red NAS drives - they cost a little bit more, but the 3TB version can usually be had for $140-160 and they are worth every penny.
I used to run a Windows Home Server setup, and this is MUCH easier to work with and add drives to - especially after Microsoft removed the Drive Extender feature in WHS 2011.
I have 12 drives in the unit currently (Using the DX513 expansion module as well) and it takes about 24 hours to add an additional 3TB drive. BUT, this is a ONE TIME ordeal and the system is accessible and usable the entire time.
I bought the Synology to replace an older NAS server. It works great, is easily expandable and is easy to set up and maintain. I recently added the expansion unit which was a seamless add on. I highly recommend this if you are looking for a home office or business application.
This is a great add-on to a  1812 or a 1813 to expand storage space with no hassles! It just worked seamlessly!
Amazon did a great job in handling the return. The exchange unit arrived in just two days.ORIGINAL REVIEW: This DX 513 arrived with only Bay #1 detecting a drive. I swapped five identical drives among the slots, and confirmed that all other four bays would not detect a drive. I called Synology tech support and they suggested an exchange. Amazon return was swift and a replacement unit is already on its way. I have to rate it one star for now because of poor quality control.
I am updating this review after identifying a fix. When the exchange unit arrived with exactly the same problem (four out of five bays do not work), I decided to search for firmware update for, not the DX513, but the DS1511+ that the DX513 is connected to. The tech support at Synology apparently does know their own product. It seems that the real issue is that the DSM on DS1511+ needs to be updated from its 2011 version 3+ to the current 4.
A great way to expand your Synology system; however, the way Synology expands the server size, it takes a long time (days) to bring the expansion unit on-line. There are also known issues that can cause an expansion failure. Luckily, the failure doesn't affect the data one already has on the main server - one just has to start over on adding the expansion unit to the primary server. It was a bit frustrating, but still worth five stars once it is up and running.
Pro: install including unboxing 60-90 seconds, Synology 1512+ recognized it on first boot, once you locate the area in Sys manager it has a good (4/5 stars) setup wizard, took my 5 western digital red 2TB drives with no need for new software or drivers, and once the raid 5 was started it finished with no problems.Cons: expensive but if you have a synology that will take it, it's a good deal. Getting to the Raid wizard needs to be easier.
Added the Disks, Plugged it in and it worked. This was the 2nd DX513 I added to increase the storage on my disk array.
Answer: Depends on what is the desired effect.  DS413 holds 4 drives and can only use DX513 as external storage (i.e. not fully).  DX513 is ideal for adding drives to existing fully compatible systems (not those limited to external storage) when they run out of drive bays; the resulting RAID volumes will span across physical modules in the sense that when a compatible Synology system with N bays adds a DX513, it can have an N+5 drive array as a single volume (or as multiple volumes).  A new DS414 will still have only four drive bays (same as your current DS413) so you would not gain more storage bays by replacement of DS413 with DS414.  For example, with a DS713+ and a DX513, you can have a 7-drive array.  Synology compatibility list is here  https://www.synology.com/en-global/products/DX513#spec