Is trying hard to get many large VCs to invest in your company or using something like AngelList to get many smaller angel investors?
What are the pros and cons of each approach?
They're different options for different situations. With the exception of seed-stage firms, VCs generally want to invest seven figures or more into startups that have achieved product-market fit, and have discovered the main levers they can use to drive their marketing. It's an investment made when there's a clear "money in -> results out" proposition.
Angel investors exist for startups at the beginning (pre-product, pre-profitability, or otherwise pre-ready-to-scale). Without a track record of success that would let them get more funding from VCs, startups instead need to raise a smaller "seed funding" round from angel investors or a seed stage VC, to provide some operating capital, allow for the first few key hires, and have some budget to start bringing in results from marketing channels that work. It's typically an amount less than $500,000.
Assuming you're in a situation where you're choosing between an early stage VC and a set of angel investors for an early-stage investment of $1,000,000 or less, here are some things to keep in mind: