From personal observation and limited research on the topic, it appears that when considering vendors to hire, companies use some common elements, but vendor size isn't always one of them. For example, at or near the top would be Right Product Capabilities -- knowing that the vendor's product/service fits the goals and needs of the buyer.
In the next tier would come (order will vary based on company and situation):
- Technical Skill (for support and design)
- Capacity/Scalability The buyer company is not only growing and changing, but may also try out a new vendor with a small piece of business before ramping up the purchase.
- Competitive Pricing - the sum of vendor costs help keep the buyers competitive in their own markets
- Reputation/Brand counts, but often more as table stakes in B2B -- such as assuring financial stability, that the vendor stands by its work, etc.
Let me offer a few hypotheses regarding the impact of vendor size in the consideration and selection of vendors by many B2B companies.
1. There's a rule of thumb or "sweet spot range" on supplier size -- not too big or too small, (as measured by the percent of business the customer represents). If too small, say less than 1% of the supplier's business, and some believe you won't get enough attention. If too large, say over 10% of their business, then they may be over dependent on you and less able to withstand fluctuations in your volume (down or up). Here is one source supporting this notion and advising buyers to stay within the sweet spot range in picking vendors.
2. Bigger customers will look for big-enough vendors -- a minimal threshold to be of adequate size and/or brand/reputation to be considered. Part of the thinking has to do with Capacity/Scalability, but the other part is risk management for the company and the decision-maker. As the saying goes, "Nobody got fired for hiring IBM." Fewer are questioned in the corporate world for hiring a supplier of size and standing.
3. Bigger customers will lean toward smaller vendors as long as they are big enough (meeting other criteria). This is really a corollary of hypothesis #1. Large companies have been accustomed to being treated as major accounts with leverage in their supplier relationships. So they would rather represent closer to 10% than 1% of their vendor's business. This often means working with vendors that are not the largest in the sector.
For vendors, one implication is about marketing strategy -- realizing where the best match-ups might be in targeting customers, given your size. Also running through all the vendor choice criteria is the need to be customer focused. For example, as a market leader, vendors will have to remain nimble in order to compete with the smaller and ofter hungrier vendors in their space. They will also have to sell the buyer that they can "act small" in their customer focus and flexibility.