The name 'Hillel' means 'praised'; the name 'Shammai' means 'appraiser'. I wonder if thee meanings correlate to the positions ascribed to them - with Shammai more inclined to evaluate things as the truly are and Hillel inclined to allow for generous leeway. A few of their famous disputes seem to go in that direction:
- The well-known dispute of 'KeitzadMerakdin', in which the Hillelites instruct that every groom must be praised for his choice of a bride, whereas the Shammites ruled that a spade must be called a spade.
- The Shammites placed a 'real' value on kiddushei kessef, whereas the Hillelites placed a symbolic value.
- In the set of three narratives about potential converts who approach Hillel and Shammai, Hillel is willing to look beyond the present reality, whereas Shammai looks at the present situation; indeed, Shammai chases one prospective convert out with a yardstick. (I discussed this set of narratives here and here).