They are both quite sluggish until you get to the foothills and contain some cracking trophy fish, some of the largest browns I have seen have been in these rivers, BUT they are SOOOOOOOO wary in the crystal clear water and pretty unforgiving to anything but the very best presentation. The water is quite barren, with super long glides and spotting crusing fish is the best option with a careful intercept, they are not easy rivers to fish at all.
In the upper reaches the Okuru is heli-guided frequently and is easy going once through the gorge. They both have some nice spring creek tribs. There are no fish above the power station on the Turnbull. If in the area also check out the Waita just north of Haast, lovely small stream with good numbers of fish in the lower reaches up to the Maori conf. Have also had some great days on the Jackson, but the fish numbers have really declined in the last few years, the mid reaches are best and the road follows along much of it's length through to the Cascade (now theres a wicked river!!!), super sight fishing, but the fish are in average condition. In the lower reaches above where the jetboats put in contains the best numbers.
Fishing streamers to sea runners in the very lower reaches will be your best bet, there is easy access from the road bridges to the more prolific esturaine water. You won't need a big cast as the runners tend to feed on the Whitebait right on the edges. I prefer a floating line, on a 5wt, cast across and slightly down and twitch in with the little current, slightly weighted Smelt patters are the go. Clark can show you some of his creations which would work a treat. I'd use a heavier tippet around 6lbs as they can hit quite hard.
As you say, when the Whitebait are running, both the Turnbull and Okuru offer some of the best sea-run fishing in NZ, the Mullet are also prolific and will also hit streamers with gusto.
This is the Okuru (mid reaches) below earlier this year, you can see why the conditions work in their favour...
And this is the Jackson, just down the road.
Andrew