I'm Federal Government and our policy is now "Lowest Practical Fare"
What this means is that we have to choose whatever is cheapest giving consideration to the circumstances. So there's a bit of flexibility there. We have a dedicated booking portal provided by a travel agency and it will show us what's available to us (no Tiger) but for most staff we have to fly Y everywhere. The price difference on Gov fares between Restricted and Flexible airfares is usually very small and if it's a busy day sometimes the Restricted tickets will even cost more, so if there's a chance our plans could change at all we'd book the Flexible ticket because the extra cost is almost always smaller than the change fee on a Restricted ticket. For me, I'm usually travelling for meetings etc. that are frequently rescheduled, cancelled, rescheduled again etc. so unless I'm
certain it's going to go ahead I'll go for the flexible ticket.
For me I almost always travel VA because for the SYD-CBR run their Gov Flexible fares are a little cheaper than QF, but they have a lot less frequency on that route so I have to watch out that I'm not saving a few dollars on airfare but costing a lot more in travel allowance because the schedule will result in me being stuck in the airport for an extra few hours. This sometimes requires a bit of maths on my part before I decide which flights will be best.
Overall I think the policy does strike the right balance between securing the cheapest airfares but giving us some flexibility to ensure we're not wasting money in other ways because we're compulsively chasing a few dollars off the seat.
When it comes to hotels we have a booking portal that shows us Gov rates and limits us to a per-night rate set for each location by the ATO. We can override the rate under certain circumstances (like staying at the hotel a conference is being held at to save on cab-charge) but usually we'd just stick to below the limit. We do get flexible cancellation rules with Gov rates, so that's pretty handy. The limits set by the ATO, however, can sometimes lead to some odd results. For example there's a different rate in Canberra and in Queanbeyan, even though for travel purposes they're basically the same place. Also, the rate limit doesn't change just because it's a sitting week for Parliament and everything is booked out and very expensive.
Also, while this is fairly consistent across Fed Gov (and if you love policy docs you can find all this info and more at the Department of Finance's website) it isn't universal and some departments and agencies (depending on how Gov procurement rules apply to them) may still have their own arrangements (particularly for hotels) rather than going in on the whole-of-gov arrangements. Also, it's a little known fact that the first whole-of-gov arrangement for travel only happened in 2010 and before that every agency and department was just doing its own thing.