These are valid questions, but depending on who you ask you are very likely to get a different answer. I'll try to answer from an SSL VPN developer standpoint.
In the VPN world there are two main types of deployment, the 'site-to-site' and the 'remote access' types. To put it simply, the first is about securing lines between two offices, and the latter is about securing the connection between your remote users and the office. The former type may rely on some minimal PKI deployment or pre-shared keys, but the latter requires integration with some user database, credentials, as well as settings which may be applied individually for each user. In addition the 'remote access' type is often associated with accounting such as keeping track how long a user is connected, how much data has been transferred and so on. That may remind you the kind of accounting used in ppp and dial-up connections, and indeed the same radius-based accounting methods are being used for that purpose.
Both of the 'site-to-site' and 'remote access' setups can be handled by either SSL or IPSec VPNs. However, there are some facts that make some VPNs more suitable for one purpose than the other. In particular, it is believed that SSL VPNs are more suitable for the 'remote access' type of VPNs, while IPSec is unquestionably the solution one would deploy on site-to-site connections. In the next paragraphs I focus on the SSL VPNs and try to list their competitive advantage for the purpose of 'remote access'.
- Application level. In SSL VPNs the software is at the application level, and that means that it can provided by the software distributor, or even by the administrator of the server. These VPN applications can be customized for the particular service the user connects to (e.g., include logos, or adjust to the environment the user is used to, or even integrate VPN connectivity with an application). For example the 12vpn.net VPN provider customizes the openconnect-gui application (which is free software) to provide it with a pre-loaded list of the servers they offer to their customers. Several other proprietary solutions use a similar practice, and the server provides the software for the end users.
- Custom interfaces for authentication. The fact that (most) SSL VPNs run over HTTPS, it provides them with an inherent feature of having complete control over the authentication interface they can display to users. For example in Openconnect VPN we provide the client with XML forms that the user is presented and must fill in, in order to authenticate. That usually covers typical password authentication, one time passwords, group selections, and so on. Other SSL VPN solutions use entirely free form HTML authentication and often only require a browser to log to the network. Others integrate certificate issuing on the first user connection using SCEP, and so on.
- Enforcing a security policy. Another reason (which I don't quite like or endorse - but happens quite often) is that the VPN client applications, enforce a particular company-wide security policy; e.g., ensure that anti-virus software is running and up to date, prior to connecting to the company LAN. This often is implemented with server provided executables being run by the clients, but that is also a double-edged sword as a VPN server compromise will allow for a compromise of all the clients. In fact the bypass of this "feature" was one of the driving reasons behind the openconnect client.
- Server side user restrictions. On the server-side the available freedom is comparable with the client side. Because SSL VPNs are on the application layer protocol, they are more flexible in what the connecting client can be restricted to. For example, in openconnect VPN server invidual users, or groups of them can be set into a specific kernel cgroup, i.e., limiting their available CPU time, or can be restricted to a fixed bandwidth in a much more easy way than in any IPSec server.
- Reliability, i.e., operation over any network. In my opinion, the major reason of existance of SSL VPN applications and servers is that they can operate under any environment. You can be restricted by firewalls, broken networks which block ESP or UDP packets and still be able to connect to your network. That is, because the HTTPS protocol which they rely on, cannot be blocked without having a major part of the Internet go down. That's not something to overlook; a VPN service which works most of the times but not always because the user is within some misconfigured network is unreliable. Reliability is something you need when you want to communicate with colleagues when being on the field, and that's the real problem SSL VPN solve (and the main reason companies and IT administrators usually pay extra to have these features enabled). Furthermore, solutions like Openconnect VPN utilize a combination of HTTPS (TCP) and UDP when available to provide the best possible user experience. It utilizes Datagram TLS over UDP when it detects that this is allowed by network policy (and thus avoiding the TCP over TCP tunneling issues), and falls back to tunneling over HTTPS when the establishment of the DTLS channel is not possible.
That doesn't of course mean that IPSec VPNs are obsolete or not needed for remote access. We are far from that. IPSec VPNs are very well suited for site-to-site links --which are typically on networks under the full control of the deployer-- and are cross platform (if we ignore the IKEv1 vs IKEv2 issues), in the sense that you are very likely to find native servers and clients offered by the operating system. In addition, they possess a significant advantage; because they are integrated with the operating system's IP stack, they utilize the kernel for encryption which removes the need for userspace to kernel space switches. That allows them to serve high bandwidths and spend less CPU time. A kernel side TLS stack, would of course provide SSL VPNs a similar advantage but currently that is work in progress.
As a bottom line, you should chose the best tool for the job at hand based on your requirements and network limitations. I made the case for SSL VPNs, and provided the reasons of why I believe they are still widely deployed and why they'll continue to. If I have already convinced you for the need for SSL VPNs, and you are an administrator working with VPN deployments I'd like to refer you to my FOSDEM 2016 talk about the OpenConnect (SSL) VPN server, on which I describe the reasons I believe it provides a significant advantage over any existing solutions in Linux systems.