recently we installed some software updates and noticed that on the
average the values of the performance counter

PerfCounter = [\SQLServer:General Statistics()\User Connections]

increased roughly 30%. i'm trying to figure out how to measure what
might have changed (and whether i need to worry). nothing else we
measure with performance counters and graph with nagios seems to have
changed significantly (cpu, memory, full scans, batch requests, ...).

to get a handle on CPU, reads, or writes, for example, i take brief
profiler snapshots (sometimes restricted in some way, e.g. to queries
running longer than half a second), then store these to a table,
calculate a "factor" i can group by from the "TextData" of the
operations and then look at statistics such as

select top 25
[Factor], sum([CPU]) sum_cpu
FROM <table stored with profiler
group by [Factor]
order by sum_cpu DESC

but how can i get a handle on user connections?

There are Audit events for login and logout, and the logout event
has Duration, but I believe also CPU, Reads and Writes statistics.