It depends what you want to do and what you already have.
Here are some scenarios in which likely you wouldn't want Skype for Business (I'll call it "S4B" for short below) as your [main] PBX:
(1) You have a call center of any sort.
(2) You have "complicated" call flows (S4B can do time of day routing, simple menu options, ring groups of people. That's about it)
(3) Your users all "need" (*chuckle*) physical phones and you already have a lot of hardware investment in Avaya-capable phones
(4) (Similar to 3) you have a bunch of analog requirements e.g. fax, page, modem that you'd like to continue to handle through PBX
(5) You utilize a feature particular to Avaya that your users "can't live without" e.g. Service Observe. Note simultaneous ring is available in S4B, but some of the bells and whistles associate with EC500 (the ability to pull a call back to your desk, for example) are not.
(6) (Similar to 5) You have complicated needs in terms of so-and-so group needs to send this caller ID, that group a different caller ID
There might be other things that distinguish Avaya vs Skype, but start with user requirements and work from there. If the requirements end up as "make call, receive call" and basics like that Skype should be fine. Feel free to post particular feature questions and I'll try to answer. (I've administered Lync 2013 as well as Avaya)