I invest professionally through a couple funds I manage. These funds are thesis-limited: they can only invest in certain types of companies in their target sectors.
I invest personally as an angel, generally $10k-$25k, 1-5x per year. These investments are capital-limited by my personal finances.
I have dealflow which I have to evaluate for my personal and professional investing. Periodically I find great opportunities that are outside my fund sectors, and which I believe in enough to make a personal investment. Generally in such situations, I could secure a much larger allocation than I have capital for. Additionally, I sometimes have pro rata opportunities (both personally and for funds) for which I don't have capital available.
In the past, this has resulted in some great allocations going to waste. Now I'm going to try an AngelList syndicate.
All dealflow is first evaluated for the venture funds I manage. If the fund passes due to sector mismatch, but the investment looks good, I consider it personally.
If I decide to invest personally, primarily for financial return, and the company is a standard enough investment (in sector, structure, etc.) that it would fit into the offerings on AngelList, then I will syndicate it. I will not syndicate when the companies are really weird / hard to explain, if I invest for non-financial reasons, if my additional allocation is small, or any other circumstances where I deem syndication will be a pain or unlikely to succeed.
I may syndicate extra allocation from the funds I manage, but that will require additional discussions with counsel & LPs that I haven't had yet.