Your question prompts me to observe that, although I think the current guidebooks describe them as NZ grade 3 or there-abouts, there is generally a big gap between the SW Ridge of Aspiring and the Silberhorn arête on Silberhorn & Tasman.
The SW on Aspiring is really probably maybe 3- with only about 5 metres of steepish climbing on the cascade into the upper couloir (it is a bit harder if this is not well iced but you can still climb the route pretty reasonably with adequate protection) and otherwise it is mostly fairly low angle for the approximately 700m from schrund to summit with a straightforward descent.
The Silberhorn arête varies considerably through the season (and across the years). Generally you will find it much steeper, longer, more complex and far more exposed than the SW ridge. It feels much bigger again because most parties will down-climb the route. Depending on conditions you may have to accept a degree of exposure to ice-cliffs on the left of the East Face and the route can feature some quite steep & exposed sections if/when schrunds cut the ridge, but the big issue with the climb is the condition of the rock step. If iced up it is quite a fun pitch up runnels through the cliff band; if not, it is, in my view, unacceptably dangerous. The rock embodies all the (generally grossly exaggerated) things people say about rock in the NZ alps: I can think of at least one fatality, 2 cut ropes and a couple of very scary near misses associated with climbing or descending the rock step out of condition.
I think the Silberhorn arête, unless you find it in very good conditions, is probably more accurately described as 4-. I don’t think it would be unusual to find the climbing more complex than Aoraki Mt Cook’s East Ridge. I think it is a bigger outing than the Zurbriggen because it is usually steeper, icier and you have to down-climb it.
They are both fantastic routes in great positions, but rather than being comparable I think that the climb on Aspiring might be a great warm-up for Tasman.
As nominated above, the S Ridge- E Ridge traverse of Dixon is a fantastic moderate alpine route (and climbing on a lovely scale – probably about 650m from schrund to summit) and, like the Silberhorn, it is accessed from Plateau Hut. There are several slightly more technical lines rising from the Syme Neve on the W Face and on Haast.
There are some really fun moderately technical and not overly long routes around Pioneer Hut on the other side of Mt Tasman. There are lines on the Fritz Range-Mallory –Barnicoat wall that don’t get much steeper than 70 degrees and range from 3 to 7 ropelengths (there are some fun harder lines as well) and this area gives access to moderately technical-ish climbs on Haidinger, Haast (although this can be a long walk for the amount of climbing) and through mixed gullies on the towers left of the W Face of Glacier Pk. From Pioneer you can access the North Shoulder on Tasman. Its crux is less technical than the SW on Aspiring but it is a much bigger undertaking and a real classic of the park – a magnificent skywalk with great views of the lakes and plains to the East and the ocean to the West.
The biggest problem with warm up routes in NZ is they tend to use up all the good weather, so hopefully you’ve got plenty of time.