I have made investments both as a VC and as an angel investor. The distinction for me is whose money I am investing. If it's my own, usually in smaller amounts, I view it as an angel investment, even if it is a part of a round with institutional investors.
It is quite frequent that I find myself in an investment conversation that does not fit the investment vehicle I am representing at that point. This usually happens in early rounds where the amount of capital required is too small for a VC, or the terms offered are not strong enough. In these cases, I can think about an angel investment, but in my scope of activities, this can sometimes pose problems. The primary issue it brings up is whether it hurts the alignment with my investors. I try to avoid situations where it can lead to a "front-running my investors" scenario. So far, I have been successful at that.
So the ideal solution is forming a structure where a VC can participate in these types of angel rounds. Ben Horowitz has a great post on the issue and I don't need to spell out the points he already makes. I basically agree 100%.
I also think it's a great idea to utilize the Series Seed type documents in these types of deals. My latest angel investment, CivicSolar, used this set of documents which made the process considerable faster, and I presume, less expensive for CivicSolar.