I have a client who is a medium-size company with about 150 employees.
 80 of those employees are call center agents and the client would
like to switch to VOIP for their phone service (i.e. a software-based
VOIP system).  Note that they DO NOT want VOIP service outside their
office, just inside their office.  They are a finance-related company
and VOIP is not secure outside their network.

I am currently looking at Cosmocom, Interactive Intelligence and
Telephony at Work.  We need robust reports, unified messaging, call
recording, predictive dialing and other typical features of VOIP
systems.  Can anyone provide me with a market share listing of VOIP
systems?  In other words, I need a listing of the market share of
companies that develop VOIP systems.  I'm trying to get answers to
questions like, "Is Interactive Intelligence a big player?" or "Does
Cosmocom have much market share?".

Interactive Intelligence is definitely a big player.  They have been
doing this for a very long time (relative to VOIP's existance and
everyone else).  Interactive Intelligence's CIC system is well know in
the Call Center world.

VONEXUS, their subsidiary partnered with Microsoft, is a small
business solution that brings all the feature rich CIC offerings into
an out-of-the-box, easier, CHEAPER, VOIP solution.

Vonexus is based on Intel's HMP software (that provides the
voice/fax/conference resources).  That's right, a SOFTWARE solution,
which means if you need more phones, you just order more software
licenses.  You can use whatever SIP phones you want OR (for the
cheapest route) you can use simple USB headsets, because Vonexus has a
built in "softphone" client for every workstation.  Other PBXs are
hardware, so they have limited expandability and require you to buy
THEIR expensive phones.  One day your business grows and a new
employee needs a phone, but that means buying a bigger system and your
old one you spent all that money on is worthless.

Some nice features with Vonexus:
   1.) Switchover: Offers redundancy, so if your primary server goes
down you seemlessly switchover to the backup.
   2.) Multi-site: This allows you to have offices in many different
locations all part of the same "network".  The users can be placed
into workgroups that span different locations.
   3.) Record a call, all calls, monitor other calls (if you have those rights).
   4.) Presence:  You can set your status, and see the status of
others (available, away from desk, in a meeting, out of the office, at
lunch, etc. and make your own.)
   5.) Unified messaging, and email integration.  Someone calls your
voicemail, or perhaps you see their call alert you so with one click
you send them to your voicemail.  Their message is compressed,
attached to an email and sent to you immediately.
   6.) Robust reporting (full array of reporting).  You can also
create your own reports with Crystal Reports.  .rpt files.
   7.) Interaction Tracker, so you can easily search through your
interaction history.  (Calls, emails, chats, SMS messages...etc).
   8.) ACD call routing: Calls can go to a workgroup and are
intelligently routed to the best agent via skills assigned, time
available, etc.
   9.) Transfer or Create Conferences by simple drag and drop.
  10.) Attendant: too much to explain, but it is easy and very
customizable so you can fully control your main menus, greetings, call
routing, etc.

Vonexus is a Software solution, built with SIP standards for VOIP, on
a Microsoft platform, and integrates into every Microsoft small
business product under the sun.

I seriously feel they are hands down the best for VOIP small to medium offices.