Based on the tng technical manual mostly from the graph on page 55, the power vs speed vs fuel usage can be calculated.
warp field mechanics dictate that fields are made up of layers. The faster you go the more layers you need and the harder it becomes to maintain each one. (per layer (cochrane), Exp 3 for warp 1 and Exp 8 for warp 9, in millions of joules).
At warp 6, at 390 cochranes at 1 EXP 6.6 mega joules per cochrane is 1.55 Quadrillion Joules. At warp 9, at 1516 cochranes, at 1 EXP 8 per cochrane, is 151.6 Quadrillion Joules.
Assuming joules are watts, a ship travelling at warp 9 would burn 3.3kg of fuel a second (at 51% coil efficiency, Energy of 302 EXP 15, divided by C squared is 3.3 approx) and at warp 6 would burn 0.0172kg a second (at close to 100% coil efficiency).
Warp Energy physics also dictactes that the ratio of matter to antimatter changes with warp factor. 10:1 for warp 1, and 1:1 at warp 8 and above.
with a standard cruising speed of warp 6 for 3 years, a ship would go through about 1.63 million kilograms of fuel with about 1/5 being antimatter (a 4:1 matter-antimatter ratio for warp 6). with 326,000 kilos of antimatter and a ratio of 1:1 a ship would burn through this at warp 9 in just 54.9 hours or 2 days.
so 3 years down to 2 days, depending on how fast you are going, and what region of space you are in. (subspace instabilities cost more energy to travel around as the warp field is much harder to maintain). the antimatter generator is for emergency use only (usually if you've encountered an anomaly that has neutralized the anti-matter) and would only provide enough to limp to the nearest starbase, a few kilos at most.
This also explains that the klingon sleeper ship would have been travelling at a low warp factor. Travel times between close stars taking decades requiring stasis, instead of the few days it would take a tng-era ship.
As in real life, speed for a starship comes at the cost of fuel and fuel efficiency.