My workplace recently(~a year ago) switched to Skype for Business. We were using Microsoft communicator before this. Skype came in with Office 365 update.
I like that it integrates well with Outlook. You can do something like create a meeting invite from within the calendar in Outlook. Then when meeting reminder pops up it will automatically contain a link the invitee can click on to join meeting remotely via Skype things like that make teleconferencing etc dead easy.
There are some other pretty nice features like being able to see someones Skype status from outlook when you read email. i.e so you know if they are at their desk or working remotely etc.
It is also simple to do things like sharing a screen, we use this feature a lot for remote meetings. There are a heap of non technical people in my org and screen sharing was always a huge pain point in the past.
I haven't noticed the issue with timestamps but no one in my org really uses the messaging/chat features everything here has traditionally been email based so I've never seen many missed conversation messages. The only thing conversations are used for are quick fire stuff like "Are you coming for lunch?" and even then 90% of people still use email or phone for this.
One horrible bug I have noticed is Skype will email me when I have a new voice mail and it uses some horrible speech to text conversion to describe what is in the message which results in what is essentially nonsense.
Bad voice mail auto translation have become a kind of office meme around here with people sharing the funniest ones etc. I do not think their speech to text understands Australian accents at all...