There isn't going to be a single answer to this question as it will always depend on your application requirements and your compliance obligations. Companies like F5, A10, Citrix offer services that expand well past basic load balancing and offer features lb just cannot touch.
If you're JUST looking for lb services and maybe some SSL bridging or offloading here are some benefits:
- Hardware: Offer hardware accelerated SSL offloading and bulk encryption due to the use of FPGA services. This is also dependent on what cipher suites you plan to use. With hardware you're usually placing them in front of 100's of applications or you're using it because they may be certified firewalls and you need additional requirements for compliancy.
- Software: If you just need basic LB, HAProxy/Nginx are an easy choice for basic lb services and even some SSL services. Support is mixed if you're not paying for it, having to rely only on community examples.
However, if you have mixed environments and maybe already have 1 vendor in play, that can help decide. All of the hardware vendors offer virtual appliances and have automation tools to help with elastic environments so really it ends up being "Will you only ever need LB services or will you end up having to tack on more later"?
The F5/A10/Citrix ADC's in cloud still offer more features in a single platform than having to spin up segregated services (think firewall/load balancing/Web firewall/global load balancing/fraud prevention/analytics/access management).
Updated 6/21/2017:
Hardware: People are buying hardware solutions not to proxy 1 or 2 applications but 100 or 200, or even 1000 or 2000 applications in their data centers (on site or collocated). For these cases it's about performance and services beyond lb. It includes security needs and app protection that are not baked into HAproxy and Nginx.
ADC Vendors Software Solutions: You have 3 options because F5/A10/Citrix also sell virtual appliances allowing you to run the same software in Azure/AWS/Google or in VMWare.... you get the idea. This becomes unique because you can have hardware in your co-location and virtual appliances in your cloud solution and its the same vendor and the bonus for your admins, the same support escalation point.
HAproxy/Nginx Softare: This goes back to the original statement, if you're talking LB solution only and price is a concern, this is your way to go. The feature sets are more limited than the ADC/Security solutions above, but they do LB justfine. It can become a bit cumbersome managing 100's of apps so you'll have to rely on your dev team a bit more to make sure they're isolating environments OR are REALLY good at automation.
The decision comes down to will you only need load balancers? If yes, then HAproxy/Nginx. If you need more features to load balance AND protect your app, then ADC software solutions are the way to go.
If you need reliable performance and cannot justify dedicating one vm per host to achieve it, then hardware ADC's are the way to go.
For transparency, I work on the DevCentral team at F5 so I would love to say go hardware, but if you don't need it don't do it. But its going to come down to your application requirements.