I have experience with Kemp and Loadbalancer.org. One of the advantages of LB.org (if you're a Linux bod), is they don't lock down root access to the unit, you can access via SSH by default (obviously you can tighten up the security later), and the support team is very helpful when it comes to bespoke requests such as custom firewall rules, and health checking scripts (on the load balancer).
Software-wise, these load balancers are pretty similar. Kemp/Load balancer use LVS (which is part of the Linux kernel and hence very fast) for the core layer 4 load balancing (direct routing and NAT). CoyotePoint may use FreeBSD, but you'd have to check this. F5 switched from FreeBSD to Linux fairly recently. For Layer 7 Loadbalancer.org uses HAProxy and they have actually contributed back to the project (see http://haproxy.1wt.eu/contrib.html). I'm not sure if Kemp uses HAProxy, but they may use a proprietary solution, and I'm pretty sure Coyote point's L7 stuff is proprietary. All offer similar features, such as cookie insertion, RDP cookies, URL switching etc.
All three come with a web user interface (WUI) for management and essentially these are writing to the config files of the various software components, such as LVS/HAProxy/Stunnel (for SSL termination), network interface files, etc. etc. They will also help you set up health checks and monitor CPU/mem/disk/network usage.
If you are very particular about the hardware, I suggest contacting the companies directly for specs (such as the processor model etc). If you're interested in SSL termination, this blog post may be of interest:
Best way to trial is to download a virtual appliance and run it in VMWare ESX or similar (both Kemp and LB.org offer this for 30 days).
I have no personal experience with Coyote but I've heard pretty good things about their units. I think generally it comes down to the quality of the support and the maturity of the underlying software; LVS and HAProxy are both well established and used on some huge websites. This website uses HAProxy along with the rest of the Stack Exchange websites, not to mention Twitter and Github among others:
so I think it bodes well that LB.org are using it and contributing back; it makes a lot of sense to make use of an existing active community.