Really doubt there is any real difference in the detector's performance, with fresh, most expensive, disposable batteries, and cheap rechargeables. Runtime should be the only issue. Have to be a really poorly, and under powered device, to have issues. You need a stable, regulated power source for digital electronics.
For me, rechargeables work fine, I only hunt, maybe 2 hours or so at a time, get several hunts, before recharging. Some people hunt all day, may need to swap out batteries out in the field. Runtime might be an issue for these people, specially if they are in some sort of sport competition. I just hobby hunt, just for fun, just for me, not looking to get rich, or racing against a credit card bill. Throwing away an 8-pack of AAs every month just doesn't make sense to me, annoying to remember to keep buying them, or have to make a special stop, before I can go out for a quick hunt. Chasing those sales...
Rechargeable batteries are a little different, you have to take care of them, if you want them to last a long time (years). If you run them, until they die, leave them sit around for weeks, until you are ready to hunt, before charging them. you are going to reduce the lifetime of those batteries. They do best, if kept charged. Those timer-based chargers, specially those "Fast" chargers, are also lifetime killers, the let the batteries get hot, which damages the chemistry. The battery companies don't want you to use the same set for years, they want to keep selling you more batteries. I'm going on 4 years, for the same set of Duracell batteries I bought for my Tesoro DeLeon. I've used other batteries occasionally, if I have some handy, but don't see any functional difference in the detector. Alkaline batteries last considerably longer, then you throw them away.