Scholarships mean better talent. Most schools also have much better facilities like larger stadiums and more resources in general. Better players will gravitate here, period.
Division 1 teams can offer up to 18 scholarships. Schools have the option of splitting them, such as two half scholarships. Most (all?) teams don't typically go into details of how they break them down. Some leagues may differ though. For example, teams in the Atlantic hockey league are smaller and go for more cost control by limiting it to 12 scholarships. The NCAA also created a limit. D3 schools that play up at D1 can't offer scholarships, like RIT. Schools doing so prior to the rule are grandfathered.
The best players go for D1, but a small number of lower D1 schools may lose to top D3 teams. They don't play that often though so not much to compare. Huntsville is a rare exception. As the only southern school, when their last league disbanded in 2009, no one wanted them in a new league. With no clear path to the tournament, they struggled to get quality recruits. A previous school administrator even dropped the team for a bit until they were saved. When they scrambled to come back, that resulted in scheduling club teams and D3 teams to fill out a schedule. They have now been accepted into the WCHA for next year which should help quite a few problems. Obviously an unusual case. Most D1 teams will beat D3.