The position of the senior systems engineer is likely to require more construction and design tasks than a standard systems administrator job. Both jobs have responsibilities for the day-to-day management and maintenance of storage and servers, the senior engineer may be the person who first came up with the system; this could vary from selecting the server platform, to information regarding processors, RAM, and networking cards.
In addition to the general Windows/Linux servers, an experienced systems engineer is likely to have specific expertise. Common specialties include storage (with special attention paid to specific companies such as Netapp, Hitachi and EMC being the most popular) and virtualization (Vmware Vsphere first, then Hyper-V) or specific large-scale platforms. The large-scale platform specialties, like SAP or SaaS are a good way to make the options for job seekers less diversified (whereas virtualization and storage are more general) however, it frequently leads to most secure and lucrative jobs.
The most experienced senior engineers in systems typically have been exposed to multiple aspects of the world of systems. A good senior engineer working in the Windows shop should have at minimum, some experience working with Active Directory, Exchange, storage, virtualization, basic network (ideally Cisco), at minimum one antivirus software as well as at least one enterprise-level backup solution. If you're using the case of a Linux or Unix Environment, the list is similar with the exception of substituting Active Directory with Samba/EDir and Exchange with something similar to Zimbra. Due to the fact that an experienced senior engineer is in charge of designing platforms instead of merely managing them in a continuous manner, their vast experience of their work ensures they have the expertise required to develop concepts for new platforms and projects.