If you took sharp photo of pump and posted, folks here could probably tell you brand. That's what I think you mean when you say you don't know what "kind" you have. My bet is that you have Bennett which has long been quite popular. But I know what you are asking, that is an opinion from someone who has had both types about their durability, operation, and ease of repair.
One con I can see with hydraulic type is that they can develop leaks which requires hose changes. I've never had that problem to my knowledge and they just keep chugging on.
Joel Albert, Potomac MD
"Charlie B" - 1988 32' FBS
Twin 318's/FWC/16x15 nibral props
docked Deale, MD