Like a lot of RF engineering, the answer depends on a lot of factors.
The loss by the matching network is usually called "insertion loss." However, with most antenna tuners, the loss varies greatly depending on the antenna impedance. SWR of 3 is not very bad, but it can be 17 ohm real, or 150 ohm real, or it can take uncountably many values of complex numbers.
The discussion below assumes all tuners are built with the best commonly available components (either available now or in the past half century even though they may not be obtainable today).
The lowest loss network is L-match. The problem with L-match is that it requires a huge range of capacitors and inductors, so it is only practical with relay-driven ATUs. The insertion loss is probably in the range of 0.15 to 0.25dB or something of that order for all cases of SWR 3.
The worst is probably Z-match, especially on high bands and high impedance load. Z-match can lose more than 3dB, and the best case loses 1dB or so. It is difficult to improve the insertion loss of a Z-match with any resonable effort to improve the component and build quality, so this topology is limited to QRP uses (or the heat from the loss will be destructive).
T-match is decent for the high-impedance side but gets poor for low-impedance loads and also on low bands. The insertion loss of T-match greatly depends on the quality of the inductors and the range of the variable capacitors used. Larger Cmax is better, especially for the output/load-side capacitor.
Much lesser known, but pi-C match is a bit worse than L-match ATUs but it is a very usable manual tuner topology, and the loss is relatively constant regardless of the load impedance. The insertion loss is typically on the order of 0.3 to 0.5 dB, depending on the design spec (maximum SWR to match) and component/build quality.
